







A question about perfect squares 
20180204 

From Jolyn: Find the smallest possible value of a whole number m if 648x m is a perfect square Answered by Penny Nom. 





27000001 
20171009 

From Tulashiram: If a× b =27000001, then what is the value of a & b ? Answered by Penny Nom. 





Factors 
20170816 

From Gemma: Why do 315 and 525 have the same number of factors? Answered by Penny Nom. 





The product of a 2digit number and a 3digit number 
20150206 

From Nathaniel: The product of a 2digit number and a 3digit number is about 50 000 what are the products Answered by Penny Nom. 





Mutually prime composite numbers 
20150109 

From nivedita: Two composite number that is mutually prime? Answered by Penny Nom. 





The units digit of a prime 
20150108 

From Patricia: Every prime number greater than 10 has a digit in the ones place that is included in which set of numbers below 1 3 7 9 or 1 3 7 or 0 2 4 5 6 8 or 1 3 5 9 Answered by Walter Whiteley. 





Prime factorization in exponent form 
20141031 

From Emma: I need to find out how to make a prime factorization of 120 in exponential form. Answered by Penny Nom. 





Sieve of Eratosthenes 
20141003 

From Hope: using Sieve of Eratosthenes to determine for in instance prime numbers between 1 to 200, to what nth number should i stop?, 4th, which is 11 or what? Answered by Robert Dawson. 





Prime factorization 
20140206 

From Kadeejah: Write the prime factorization of 37 in exponential form Answered by Penny Nom. 





GCD 
20130520 

From Julia: Prove that if a and b are coprime integers, the greatest common divisor of a + b and a  b is either 1 or 2. Answered by Penny Nom. 





A four digit number 
20121009 

From cyndi: find this 4 digit number: the tens digit is 1/3 of the hundreds digit; the 2 digit number formed by the tens and ones digits i the largest prime number smaller than 40; the sum of all 4 digits is the same as the number of face on an icosahedron ? what is the number? Answered by Penny Nom. 





What is the prime factor form of 7/5? 
20120417 

From David: What is the prime factor form of 7/5 Answered by Robert Dawson. 





The units digit of a prime number 
20111122 

From Mike: Every prime number larger than 10 has a digit in the ones place that is included in which set of numbers below?
A. 1,3,7,9
B. 1,3,5,9
C. 0,2,4,5,6,8
D. 1,3,7 Answered by Penny Nom. 





The LCM of 6,15 and x is 90 
20111030 

From Richie: Hi there,
There are 2 parts to the question.
#1. Factorise 90. This is easy, 90=2x3x3x5
#2
LCM of 6,15 and x is 90. What are possible values of x if x is odd?
From #1, since 90=6x15, how can this be used to work out possible values of x?
Thanks in advance,
Richie Answered by Penny Nom. 





One factor array 
20110916 

From Hana: hi my brother a 5th grade have a question. this is what it say "i have only one factor array, and i am between two numbers 12 and 16. what number am i?" Answered by Penny Nom. 





What is the largest prime number? 
20101120 

From vadali: what is the largest prime number? Answered by Penny Nom. 





Powers 
20101020 

From dylan: how do you write 20736 in exponential form .same for 1728 and 50625.
is there a formula to figure out how to express large know numbers in exponential form. Answered by Penny Nom. 





Adding five positive integers that have a product of 48 
20100427 

From Lorraine: What is the smallest possible sum that can be obtained by adding five positive integers that have a product of 48. Answered by Chris Fisher. 





The cardinality of the prime numbers 
20091107 

From Justin: Hello there, I was just wondering since the number of primes is infinite,
are they equal to infinity or Alephnull?
Justin Answered by Robert Dawson and Victoria West. 





The cube of a number plus five times the number plus 1 
20091012 

From JP: Find a counterexample to the statement: The cube of a number added to the sum of five times the number and 1 is a prime number.The cube of a number added to the sum of five times the number and 1 is a prime number Answered by Penny Nom. 





What is my number? 
20090918 

From Hanna: What is my number?
My number is a perfect square.
The only number in its prime factorization is 2.
My number is a factor of 32.
The sum of its digits is odd. Answered by Penny Nom. 





Exponential form 
20090831 

From cecil: what is the exponent form 564000? Answered by Stephen La Rocque and Harley Weston. 





Primes 
20090625 

From Chinonyerem: If p = 2^k  1 is prime, show that k is an odd integer, except when k = 2.
[ Hint: 3/4^n  1 for all n >= 1.] Answered by Robert Dawson and Penny Nom. 





GCD (a + b, a  b). 
20090401 

From Tomas: Let a and b integer and relatively prime. Prove that:
GCD (a + b , a  b) = 1 or 2 Answered by Stephen La Rocque. 





The factors of an integer 
20090106 

From Madison: what are the factors of 878 Answered by Robert Dawson. 





Do all square numbers have an odd number or factors? 
20081211 

From Amy: Do all square numbers have an odd number or factors? Answered by Victoria West. 





Some number theoretic speculations 
20081204 

From Andrew: Another way of looking at the 'alternating parity polynomial', again based on Fermat's Little Theorem,
is to substitute (a  b) for x in x^(p1)  1 as this is always divisible by any prime p. So, if one removes
the " 1", there is always a remainder of (1/p)! (I took up your challenge!)
. . .
Andrew Answered by Chris Fisher and Victoria West. 





Primes and polynomials 
20081124 

From Andrew: How effective are the two
pairs of polynomials, taken together, at "excluding" any prime p.
1. (a^2  a.b + b^2) and (a^2 + a.b + b^2) Where b > a > p and (a, b, p) = 1
2. (c^2  c.a + a^2) and (c^2  c.b + b^2) Where c > b > a > p and (a, b, c, p) = 1 Answered by Victoria West. 





A question about primes and polynomials 
20081116 

From Andrew: Is it possible for (a^2  a.b + b^2) to be divisible by a prime p where
b > a > p and a, b, and p are relatively prime? I let a = n.p + x and
b = m.p + y (where both x and y are < p) and after dividing throughout
by p one gets to decide whether (x^2  x.y + y^2) ==0 mod(p) ?! It seems
unlikely unless p = (x^2  x.y + y^2)? (Note: All letters represent positive
integers.) Answered by Chris Fisher and Victoria West. 





The prime factorization of one billion 
20081102 

From Alta: The prime factorization of 1000 is 2 cubed times 5 cubed. How do you write the prime factorization of one billion using exponents? Answered by Penny Nom. 





Prime factorization 
20081019 

From nick: while im doing prime factorization for one number and it cant be divided 2,3 or five so what next? Answered by Penny Nom. 





Product of TwoDigit Numbers 
20080731 

From pete: The number 4641 can be expressed as the product of two twodigit whole numbers. What is the sum of these two numbers? Answered by Janice Cotcher. 





Neither prime nor composite 
20080708 

From saloni: Give the counting number which is neither prime nor composite ? Answered by Penny Nom. 





The square root of (18*n*34) 
20080701 

From Peter: What is the least possible positive integervalue of n such that square root(18*n*34) is an integer? Answered by Penny Nom. 





The smallest number divisible by 1 to 9 
20080626 

From Peggy: What is the smallest number divisible by each of the first nine counting numbers? Answered by Penny Nom. 





Prime factors 
20080521 

From john: the first 5 prime numbers are 2,3,5,7,11. which is the smallest number that has these prime factors. Answered by Stephen La Rocque. 





Why is the number 1 neither prime nor composite? 
20080207 

From ronni: why is the number 1 neither prime nor composite? Answered by Harley Weston. 





A positive integer with 2007 digits 
20080206 

From Tom: Prove that there's a unique positive integer of 2007 digits lenght, divisible by 2^2007, and made up solely by the digits 2 and 5. Answered by Penny Nom. 





(1x2x3x...n)+1 
20080129 

From Sayuri: what is the smallest natural number n, greater than 1, for which (1x2x3x...n)+1 is not a prime? Answered by Penny Nom. 





Prime factorization 
20071111 

From jeff: find the prime factorization and use exponential notation for 432 Answered by Penny Nom. 





Why is the number 1 neither prime nor composite? 
20071108 

From amarilis: why is the number 1 neither prime nor composite? Answered by Penny Nom. 





I am a prime number 
20071031 

From sherry: I am a prime number. I can not be shared fairly except by one group. My array can only be one row.
array can only be one row. Can you please explain this out to me so I can help my child with it.
Thanks Answered by Penny Nom. 





An array for 31 
20071031 

From sherry: How do you make an array with the number 31 Answered by Penny Nom. 





13 year and 17 year locusts 
20071012 

From stefan: how many years pass between the years when both 13 year and 17 year locusts are out at the same time? Answered by Penny Nom. 





Cubes 
20070921 

From Yvonne: The numbers 756 and 72, expressed as products of prime factors, are 756 = 2² x 3³ x 7 and 72 = 2³ x 3²
Use these result to find,
the smallest integer, x, such that 756x is a perfect cube. Answered by Penny Nom. 





Prove that any two consecutive integers are relativley prime. 
20070918 

From Michael: Im not very good at proofs and I was wandering if you would be able to help me with the following question:
Prove that any two consecutive integers is relativley prime.
Thanks a million. Answered by Penny Nom. 





How far from n do you need to go to have found at least one prime? 
20070916 

From Mike: Hi,
I was wondering if there was some kind of guaranteed interval that ensures that if you start at some number n, you will always have passed a prime number p.
I remember having once read something that there is always at least one prime between n and 2n, but I cannot for the life of me remember where I read that, or what that kind of rule would be called so I can look it up online...
thank you for your help,
Mike Answered by Penny Nom and Victoria West. 





Prime factors in exponential form 
20070906 

From Michelle: how would you write this: factor 48 as a product of primes written in exponential form Answered by Stephen La Rocque. 





How many stairs in the flight are stepped on exactly once? 
20070903 

From Bill: Four friends are racing together down a long flight of stairs. A goes 2 steps at a time, B 3 at a time, C 4 at atime and D 5 and at a time. The only steps on which all four tread are the top one and the bottom one. How many stairs in the flight are stepped on exactly once. Answered by Harley Weston. 





Prime numbers and square numbers 
20070522 

From Naseer: I read somewhere that prime number can be a factor of square only if it occurs at least twice in its square please explian this with examples. Answered by Penny Nom. 





If the product of A,B,C is 15834, what is A+B+C? 
20070310 

From rachel: if the product of A,B,C is 15834, what is A+B+C? Answered by Penny Nom. 





Is c relatively prime to (n.p)? 
20070302 

From Andrew: Please could you help me with a small mathematics problem?! I've put = the problem into three parts but it isn't really three problems; just = one! Given: {[(n.p)^p] / [c + (n.p)]} =3D "an integer" (where c > = (n.p); c and n are integers, n is even and p is an odd prime number) Can one prove that c cannot be relatively prime to (n.p)? { i.e. c = must have the factor (n.p) ?} If so, is the converse also true? {i.e. If c is relatively prime to = (n.p), then [c + (n.p)] cannot be a factor of (n.p)^p ?} Lastly but similarly, if c is relatively prime to a and c > a > = (n.p) ; (c  a) > (n.p) **; and c is not relatively prime to (n.p) = would it be true that (c  a) cannot be a factor (n.p)^p ? I hope my question makes sense? Answered by Penny Nom. 





Three distinct prime factors 
20070215 

From nick: what is the smallest natural number that has three distinct prime factors in its factorization Answered by Stephen La Rocque. 





Why zero is neither prime nor composite? 
20070117 

From Brenda: Why zero is neither prime nor composite? Answered by Penny Nom. 





Prime numbers 
20070116 

From A student: are the product of two prime numbers always prime? Answered by Penny Nom. 





Show that 3k+2 and 5k+3 are relatively prime 
20070115 

From Andrea: show that if k is a positive integer, then 3k+2 and 5k+3 are relatively prime Answered by Penny Nom. 





The sum of prime numbers 
20061128 

From Rambabu: I would like to know the sum of prime numbers below some X say 10000. Provide me with easy way to get this done Answered by Penny Nom. 





The greatest common factor of two numbers 
20060716 

From Fadwa: What is the greatest common factor(GCF) of the following algebraic expressions? 1680 and 6048
Answered by Stephen La Rocque. 





How many numbers are relatively prime with 250? 
20060419 

From David: How many positive integers less than or equal to 250 are relatively prime with 250? Answered by Stephen La Rocque. 





given that p is a prime and pa^n, prove that p^na^n 
20060324 

From Janna: given that p is a prime and pa^{n}, prove that p^{n}a^{n} Answered by Stephen La Rocque. 





The Least Common Multiple of two primes 
20060221 

From Kristine: Is the Least Common Multiple to two prime numbers always their product? Why or Why not? Answered by Stephen La Rocque. 





How many divisors does the number 138600 have? 
20060208 

From Joe: How many divisors does the number 138600 have? Answered by Steve La Rocque and Penny Nom. 





Write the array for 3 
20060129 

From Jamie: My son is a 5th grader and came home with a math question that I can't answer. The question stated  "Write the array for 3" I don't understand how this can be done with just one number. Answered by Penny Nom. 





GCF, LCM, primes and the ladder method 
20060107 

From Linda: How would I teach both finding the GCF and LCM with prime factors...I recall the ladder method vaguely.??? Answered by Penny Nom. 





LCM 
20051212 

From Alex: what is the LCM of 210 and 54 and the LCM of 42 and 126 Answered by Penny Nom. 





Divisibility by each of the first ten counting numbers 
20051017 

From Simon: determine smallest positive integer that is divisible by each of the first ten counting numbers Answered by Penny Nom. 





A two digit prime 
20050912 

From A student: The units digit of a twodigit prime number is not greater than the tens digit by 3.If the positions of the two digits are interchanged, then the new number formed is greater than the original number by more than 18. Find the value of the original prime number. Answered by Penny Nom. 





n^2+n1 has no divisors ending with 3 or 7 
20050908 

From Arne: at least it seems like for any integers n and k,
10k+3 and 10k+7 do not divide n²+n1
I tested this for every n from 0 to 3200 (which means same for the numbers from 3201 to 1)
could this be true, or is it just coincidence, or am I just totally wrong? Answered by Richard McIntosh. 





Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: 
20050718 

From Ladis: Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: p=p, q=p+d and r= p+2d. Prove that d is divisible by 6. Answered by Chris Fisher. 





p+1, p+2 y p+4 are prime 
20050618 

From Vincent: Find all the values of p (where p is a natural number), for which the numbers p+1, p+2 y p+4 are prime. Answered by Penny Nom. 





Primes 
20050604 

From Fede: Prove that there is not a number prime p, for which the numbers p+5 and p+10 are prime too. Answered by Penny Nom. 





The numbers p and 8p^2 +1 are prime. 
20050530 

From Antonio: The numbers p and 8p^{2} +1 are prime. Prove that the number 8p^{2}+2p+1 is also a prime number. Answered by Claude Tardif and Penny Nom. 





Prime numbers 
20050411 

From Jesule: Given that p, p+10 and p+14 are prime numbers, find p. Answered by Claude Tardif and Chris Fisher. 





Numbers that John likes 
20050116 

From Garrett: John likes 400 but not 300; he likes 100 but not 99; he likes 3600 but not 3700. Which does he like?
900
1000
1100
1200 Answered by Penny Nom. 





252 x ? is a cube 
20041222 

From Andrea: What is the smallest positive interger by which 252 can be multipled so the result is a perfect cubed? Answered by Penny Nom. 





The lcm of 5, 3, 4, 7 and 2 
20041105 

From Christine: what is the lcm of 5,3,4,7,2 Answered by Penny Nom. 





an integer with three factors 
20040803 

From A student: What is the probability that a randomly chosen 3 digit number has exactly 3 factors Answered by Penny Nom. 





Divisors of 2n+1 and 3n+9 
20040602 

From Chris: Amy selected a positive integer N and wrote numbers 2xN+1 and 3xN+9 on a whiteboard. Boris looked at the two numbers on the whiteboard and wrote in his notebook a positive integer that divides each of them. Find all possible numbers that Boris could have written in his notebook. Answered by Chris Fisher and Penny Nom. 





(2^ 20,966,011)  1 
20031212 

From Reid: Can someone please explain, answer and/or solve this: (2^ 20,966,011)  1
I don't know what it means, my boss sent it out, I'm assuming it is to be
solved but don't know what it is, any prompt help would be appreciated, very
much so, in fact, thanks,........... Answered by Penny Nom. 





If 1 is neither prime nor composite... 
20031119 

From Joshua: if 1
is neither prime nor composite...what is it called? Answered by Claude Tardif and Penny Nom. 





If 1 is neither prime nor composite... 
20031119 

From Joshua: if 1
is neither prime nor composite...what is it called? Answered by Claude Tardif and Penny Nom. 





What is a number that has exactly 13 factors? 
20031109 

From Mary: What is a number that has exactly 13 factors? Answered by Penny Nom. 





Pairs of prime numbers 
20031013 

From Nikolas: Use pairs of prime numbers to find all the numbers less than 50 that have only two prime factors. Make an organized list. Answered by Penny Nom. 





Relatively prime 
20030927 

From James: what is the definition a relative prime numbers? Answered by Penny Nom. 





Primes 
20030923 

From Julie:
#1. Suppose you are given a number (n) and told that 1 and the number (n) divide into (n). Does that mean (n) is prime? #2. Suppose that p is a prime number greater than or equal to 3. Show that p+1 cannot be a prime number. Answered by Penny Nom. 





The Sieve of Eratosthenes 
20030918 

From Lynn: My daughter has been asked to find all the prime numbers by using the Sieve of Eratosthenes. I have no understanding what this means. Answered by Penny Nom and Claude Tardif. 





Making a square 
20030907 

From A student: if I am given any number (say 80 for example), how may I determine the smallest whole number integer which when multipled by it will yield a square number ? In other words if I express this as: 80Ý*ÝnÝ=ÝsquareÝnumber, what is the least value of n which will yield a square. Answered by Penny Nom. 





1575 
20030313 

From Sharyn: find 6 integers that when multiplied with each other equal +1575 and when the same integers are added together equal zero. there are more positives than negatives and one of the numbers is a double digit between 10 and 20 Answered by Penny Nom. 





X times Y equals ten million 
20030226 

From Baneen: Would you be able to tell me which two numbers would compute ten million without any number having zeros in it? Answered by Penny Nom. 





Composites, primes, factors and common factors 
20021120 

From Connie: My son can't remember what a composite number is, what a prime number is and the explaination of factors and common factors. Help! Answered by Penny Nom. 





Why is 5 divided by 1/7 greater than 5 divided by 2/3? 
20021119 

From Elizabeth:
 Without performing the division, explain why 5 divided by 1/7 is a number greater than 5 divided by 2/3.
 Is the least common multiple of two prime numbers always their product? Why or why not?
Answered by Diane Hanson and Penny Nom. 





Prime numbers 
20021108 

From Lonna: Is 2 a prime number or not?? Why is 1 not considered a prime number? Answered by Penny Nom. 





Is it a prime? 
20021019 

From JV: 6x to the third power plus 5x plus 15, is that prime or not prime, and whichever it is, how can you prove it? ya dig? Answered by Claude Tardif. 





Relatively prime 
20021004 

From Natasha: I really need help with this middle level math question. My little brother is asking me and I have no clue what the answer is. Explain what it means when two numbers are negatively prime. (?) Answered by Kathy Nolan and Penny Nom. 





Divisibility of 5^{ 2002} 
20020825 

From Simon: I need to ask you a question if 5^{ 2002} and 3^{ 2002} are divisible by 26. Answered by Penny Nom. 





Primes and square roots 
20010614 

From Paul: I have a bit of a math problem. It has to do with determining if a very large number is a prime. One method entails dividing the number by every smaller prime number. If any divide into it, it's not a prime. This would be a big job if the number was something like 400 digits long. Another way I read about was to take the square root of the number and test all the primes less than its square root. The explanation went like this: "When a number is divided by another number that is greater than its square root, the result is a number smaller than the square root. For example, the square root of 36 is 6. Dividing 36 by 2, a smaller number than 6, gives 18, a number that is larger than the square root. To prove that 37 is prime it is only necessary to divide it by primes less than 6, since if it had a prime factor greater than 6, it would have to have one less than 6 as well." I understand the explanation, up to the last sentence. I fail to see the underlying logic. Why if a prime factor exists below the square does one have to exist above the square too? The number 40 can be divided by the prime 2, a number below its square root, but no other primes can do this above its square root. Have I missed something? What's the logic here? Answered by Claude Tardif and Penny Nom. 





Neither prime nor composite 
20010508 

From Marc: what 2 numbers are neither prime nor combitative? Answered by Penny Nom. 





Probability and a three digit number 
20010315 

From Glenn: A THREE DIGIT NUMBER IS SELECTED AT RANDOM. WHAT IS THE PROBABILITY THAT NON OF THE THREE DIGITS ARE PRIME. Answered by Harley Weston. 





Two number theory questions 
20010130 

From Richie: i have two questions and they are:  the product of three consecutive prime numbers is 7429. Find the product of the smallest and largest of these three integers.
 the least common multiple of two relatively prime positive integers, a and b, is 144. if a (a>or=2) is as small as possible, compute the value of b.
Answered by Penny Nom. 





What number from 1 to 25 has the most factors? 
20010123 

From John: What number from 1 to 25 has the most factors? Answered by Penny Nom. 





A pair of numbers whose GCF is 28 
20001227 

From John: Name 2 different pairs of numbers whose GCF is 28. Answered by Penny Nom. 





Some prime conjectures 
20001224 

From Tarrasita: I was given some homework to investigate the following conjectures on prime numbers 1) There is at least one prime between consecutive square numbers. 2) Every prime except 2 and 3 is of the form 6n+1 where n is a natural number. 3) Any odd prime which is of the form 4n+1 is equal to the sum of two perfect squares. Answered by Harley Weston. 





Prime factorization 
20001213 

From A student: What is the prime factorization for 250 1296 and 2400 Answered by Penny Nom. 





A zip code problem 
20001026 

From Rob Mathis: Find the zip code of a place in a county so that the product of it and the zip code of another place in another county of the same name, but in a different state, is an exact multiple of the number 123456789 Answered by Claude Tardif. 





1234567890 
20000914 

From Bradley Kloetzly: Can you find two whole numbers, with the smallest possible difference between them, which when multipled together equal: 1234567890? Answered by Harley Weston. 





Five times a cube equals three times a fifth power 
20000705 

From Harman Chaudhry: Which is the smallest 10digit number to be five times the cube of one number and also three times the fifth power of another? Answered by Penny Nom. 





How many zeros? 
20000409 

From Greg Potts: The natural numbers 1 to 25 are multiplied together (1 x 2 x 3x..24 x 25). How many zeros are there in the product of this multiplication? a)6 b)7 c)5 d)10 or e)4? Answered by Harley Weston. 





2^32 + 1 
20000408 

From Un Etudiant: 2^{32} +1 can be divided by 641 , why? Answered by Claude Tradif. 





Symmetric Primes 
20000401 

From Marlene Moore: Hi...Im in 9th grade and am having a hard time figuring out symmetric primes. Heres the problem: Find two pairs of symmetric primes of 20. Symmetric primes of 15? Answered by Claude Tardif. 





Division 
20000316 

From Charday: What is the easiest way to calculate the least number that can be divided evenly by all the numbers from 1 to 10. Answered by Penny Nom. 





10 000 000 = a x b 
20000306 

From Spencer Jaffe: What two numbers that don't end in zero, multiplied equal 10,000,000. Answered by Claude tardif. 





Factoring, primes, GCF and LCM 
20000227 

From Ruth Kroek: My son is in grade seven, he has to do a Factoring Booklet the areas covered are:  Prime #'s
 Composite #'s
 Rainbow Factoring
 Finding Multiples (consecutive multiples)
 Finding GCF of 23 numbers uning Rainbow factoring
 Finding LCM of 2 numbers using consecutive multiples
 prime factor trees
 prime factor ladders
 finding GCF of 2 numbers using Prime number Method
Although his text 'Math Power' gives some information, we are at a loss .. Answered by Penny Nom. 





Three factors 
20000221 

From A parent: Question from a parent helping a child, grade 4, with homework. Can a number have three factors? Name three numbers that have three factors. Answered by Penny Nom. 





Three algebra problems 
19991228 

From Stephanie Branton:
 If P represents the product of all prime numbers less than 1000, what is the value of the unit's digit of P?
 Do any real numbers a and b exist such that: ln(a+b)=ln a + ln b? if so, what are they?
 Define a function by: f(x)=1/1x where x is not equal to 0,1. what is f(f(f(a)))?
Answered by Harley Weston. 





Tshirts 
19990404 

From Valerie: At a discount Tshirt shop the manager marked a special batch of Tshirts that originally sold for $2.00. When all the shirts sold the shop had collected $603.77. How many shirts did they sell and what was the price per shirt? Answered by Jack LeSage and Penny Nom. 





Prime dates 
19990325 

From Jessica Brown: I'm asking how do you figure out all the prime numbers in a year and, whats the average amount of prime numbers per week. Answered by Jack LeSage and Penny Nom. 





Five Factors 
19980919 

From Derek Yau: To whom it may concern, I have difficulty in getting the solution to the following question: Find 5 numbers that have exactly 5 factors. I got 16, 81 but couldn't find the rest. I believe that in order to have 5 factors, it has to be a square number. Isn't it true? I guess there may be a pattern to this. Thanks for your help. Derek Yau. Answered by Penny Nom. 





Divisors of 6n 
19980126 

From James: If n is a positive integer such that 2n has 28 positive divisors and 3n has 30 positive divisors, then how many positive divisors does 6n have? (a) 32 (b) 34 (c) 35 (d) 36 (e) 38 Answered by Penny Nom and Haragauri Gupta. 





Negative Primes. 
19971110 

From Leah Zucker and Paul Michael: I have received the following question via email from my granddaughter: "Can negative numbers (like 7) be prime? If not, why not?" Answered by Chris Fisher. 





Two Questions 
19971028 

From Melissa Kelley: I would appreciate any help you could give me.  Why isn't 1 a prime number?
 How can the absolute value of a number be negative?
Answered by Penny Nom. 





Prime Numbers 
19970904 

From Jack Bedard: Hi. I have a real stupid question What are prime numbers? My name is Jack Bedard and I am in grade 5. Answered by Penny Nom. 





Divisibility of 2n choose n. 
19960924 

From Kathy Doan: Can you prove that "2n choose n" is not divisible by 3, 5, and 7 for infinitely many n? Answered by Penny Nom. 





How do you find out if a number is a composite or prime? 
19960916 

From Trish Feenstra: Hi my name is Trish Feenstra. In grade 8. How do you find out if a number is a composite or prime if it is big like 37 529? Reply soon got a test on Friday the 13th Answered by Denis Hanson. 





Prime numbers 
19960222 

From Charles Hewitt: I would apprecaite it if you could share with me any algorithm to determine whether a number is prime. Answered by Penny Nom. 





Deux nombres consécutifs 
20100118 

From Janot: Bonjour
comment peut on faire pour démontrer
que si deux nombres sont consécutifs, leur produit et leur somme sont
premiers entre eux
Merci de me mettre sur la voie , j'ai échoué avec Bezout. Answered by Claude Tardif. 





2^(2^1954) estil premier? 
20051004 

From Un eleve: 2^{(21945)}+1 estil premier? Answered by Claude Tardif. 

