







The product of 3 integers is 24 
20191106 

From Rick: This is a question on my sons preap practice quiz.
I think that there is information missing (?)
The product of 3 integers is 24
The sum of 3 integers is 12
What are the 3 integers ?
This is exactly how it was written on his quiz paper.
I have wasted to much time on the internet, trying to find a
formula(s) to help him.
Please help me. Answered by Penny Nom. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





Prime factorization 
20071111 

From jeff: find the prime factorization and use exponential notation for 432 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





(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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 

