







The divisors (aliquot parts) of a positive integer 
20191031 

From Kenneth: Is there a fast and simple method that can be used to determine the aliquot parts, whole, positive numbers that can divide into another whole, positive number? Answered by Harley Weston. 





The largest integer k so that that 3335^k is a divisor of 3336! 
20191029 

From Brandon: Hello my name is Brandon and I having difficulties in solving the following question: Given the number 3336! = 1.2.3.4........................3336 . What's the greater positive integer number k with the condition that 3335expk is a divisor of 3336!
Thanks for your help. Answered by Penny Nom. 





Multiplies and factors 
20180224 

From Lil: Is a multiple the same as a factor? Answered by Penny Nom. 





GCD 
20171125 

From A student: Suppose a,b, c are integers such that gcd(a,b)=gcd(a,c)=1. Show that gcd(a,bc)=1. Answered by Penny Nom. 





Abstract algebra 
20171125 

From A student: Suppose a,b, c are integers such that gcd(a,b)=gcd(a,c)=1. Show that gcd(a,bc)=1. Answered by Penny Nom. 





Baseball Cards 
20170420 

From Raquel: A minor league baseball team gave away baseball cards to each person entering the stadium. One group receives 28 baseball cards. A second group received 68 baseball card. If each person entering the stadium receive the same number of cards, what was the greatest possible number of baseball cards that each person could have received? Answered by Penny Nom. 





The greatest common divider of n^23n1 and 3 
20140309 

From Rimoshika: determine the greatest common divider (n^23n1,3) Answered by Penny Nom. 





Two problems 
20100527 

From debbie:
Question from debbie, a parent:
hi, i have a daughter and she asked me a maths question I cannot solve. I was just wondering if you can give me the answers plus the working out so I could explain to my daughter,
1. The leftmost digit of a sixdigit number N is 1. If this digit is removed and then written as a rightmost digit, the number thus obtained is three times N .Find N.
2. Four friends are racing together down a flight of stairs. A goes 2 steps at a time, B 3 steps at a time. C 4 steps at a time and D 5 steps at a time. The only steps which all four tread on are the top one and the bottom one. How many stairs in the flight were stepped on exactly once? 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. 





Dividing seashells among girls 
20100106 

From Eileen: A group of girls collected some seashells from the beach. They tried to divided these seashells equally among them. If each girl received 8 seashells, they would need 5 more seashells. If each girl received 7 seashells, they would have 3 seashells extra. How many seashells did they collect from the beach altogether? Answered by Robert Dawson and Penny Nom. 





Dividing a number which is greater than 1 by a number that is less than 1 
20100105 

From Neda: when dividing a number which is greater than 1 by a number that is less than 1, will the quotient be greater than or less than the dividend? Explain. Answered by Robert Dawson and Penny Nom. 





Quotient 
20090914 

From Jala: What is a quotient and what are the instructions for one? Answered by Penny Nom. 





How do I divide with a decimal is the divisor? 
20090315 

From Shelly: How do I divide with a decimal is the DIVISOR ( NOT divsor AND dividend.) ? Also, How do I know when to stop dividing?
P.s. please use long division Answered by Penny Nom. 





How many students were there 
20090125 

From sooos: After a math lecture in university, the students go to the cafeteria. EACH ONE of them buys a cheese sandwich and a cup of tea. They ALL pay $18.49. How many students were they? Answered by Chris Fisher. 





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. 





A remainder of 8 
20081023 

From Kathy: When dividing a 3 digit number by a 1 digit number, for what divisors can you get a remainder of 8? is the question in my son's math book. After searching this web site, how do you explain an answer so that a ten year old can understand? I somewhat understand the answers given, but am afraid my son might not understand the answer? Help??? Answered by Penny Nom. 





Number of factors 
20080918 

From Austin: I am stuck on finding what type of number has exactly two factors and
what type of number has an odd number of factors? I need some examples. Answered by Penny Nom. 





Number of factors 
20080720 

From pete: how do you find the number of factors in a really big number without using a factoring program or listing the out? Answered by Penny Nom. 





How many positive integer factors of 2^2*3^2*5 are multiples of 12? 
20080627 

From Peter: How many positive integer factors of 2^2*3^2*5 are multiples of 12 Answered by Janice Cotcher. 





Find the smallest number that leaves a remainder of 10 when divided into 90. 
20080624 

From Peter: Find the smallest number that leaves a remainder of 10 when divided into 90. Answered by Janice Cotcher. 





What number has exactly 51 divisors? 
20080226 

From Lisa: What number has a Tau which equals 51? In other words, what number has exactly 51 divisors? It must be a square of some kind! Answered by Penny Nom, Victoria West and Harley Weston. 





Positive divisors 
20071126 

From joan: How many positive divisors of ((2^20)*(5^20))^2 are less than (2^20)*(5^20) but do not divide (2^20)*(5^20)? Answered by Victoria West. 





What are the factors of 111? 
20070913 

From Miska: What are the factors of 111? Answered by Penny Nom. 





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. 





An odd number with 12 factors 
20070627 

From Wilson: Do you know of any odd number that has 12 factors? Reply back today.
Because I have hand in a project tomorrow. Answered by Stephen La Rocque and Harley Weston. 





Students in rows 
20070517 

From Ashi: the student of three classescan be made to stand into rows having same number of students. there are 24,36 and 60 students in the classes. how many maximum number of student will stand in each row. Answered by Stephen La Rocque. 





Greatest common divisor 
20070314 

From Marie: How do I prove this?
Let h be the greatest common divisor of the positive integers a and b.
Show that there exist integers p and q (not necessarily positive) such that
pa + qb = h.
Thanks Answered by Penny Nom. 





The greatest common factor 
20061017 

From Myrna: What is the greatest common factor of 49,164 and 80,860 Answered by Stephen La Rocque. 





Find the divisors 
20060821 

From Minh: Using combination or permutation or both, find the
a. Divisors
b.even divisors
of 2160 Answered by Stephen La Rocque and Penny Nom. 





The quotient of 50 and a number is 2. 
20060817 

From Thomas: The quotient of 50 and a number is 2. Is 2 the quotient , 50 the dividend and 25 the divisor? Answered by Stephen La Rocque. 





When 391758 and 394915 are divided by a certain three digit number, ... 
20060726 

From Nick: When 391758 and 394915 are divided by a certain three digit number, the three digit reminder is the same in each case. Find the divisor. Answered by Chris Fisher and Steve La Rocque. 





x^2+2x3 is a factor f(x)=x^4+2x^37x^2+ax+b 
20060406 

From Maha: Given that x^{2}+2x3 is a factor f(x)=x^{4}+2x^{3}7x^{2}+ax+b, find a and b and hence factor f(x) completely. 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. 





GCD 
20060320 

From Jana: How can i prove:
if gcd(a,b)=1 then gcd(a+b,ab)=1 Answered by Penny Nom. 





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. 





Highest common factor 
20060206 

From Sajid:
1.A rectangular field has dimensions 156 m and 84 m. It is to be fenced with wire netting supported by stakes, equally spaced, a stake being placed at each corner of the field. What is the greatest possible distance between any two stakes, given that it should be more than 2 m and less than 8 m?
2. What is the length of the side of the largest square tile which can be used to cover a floor 525 cm long by 275 cm wide without leaving a gap?
3. Find the greatest number which will divide 140 and 249 to leave remainders 8 and 18 respectively?
4. Find the greatest number which will divide 304 and 298 so as to leave remainder 4 in each case.
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. 





For what divisors can you get a remainder of 8? 
20060106 

From Thelma: When dividing a 3 digit number by a 1 digit number, for what divisors can you get a remainder of 8? Answered by Penny Nom. 





Numbers with exactly 5 divisors 
20051123 

From Mary Lou: Show the 10 numbers with exactly 5 divisors. 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 nē+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. 





GCD and LCM 
20041031 

From Cartalina: how do you calculate the "positive difference between the GCF and LCM of two numbers"? Answered by Penny Nom. 





Some numbers less than 100 
20040917 

From Paul: for how many numbers less than 100 is the digit in the ones place half the digit in the tens place? Answered by Penny Nom. 





Crossword math puzzle 
20040914 

From Joyce and Tiffany: The puzzle name was real number vocabulary and the question is (a number that divides evenly into another what is it?). (Space in between ticmarks on a number line). Answered by Harley Weston. 





GCD (a + b , a^2  ab + b^2) 
20040827 

From Carol: Let a and b integer and relatively prime. Proof that:
GCD (a + b , a^2  ab + b^2) = 1 or 3 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. 





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. 





Greatest Common Factor 
20031108 

From Beth: How do you use the Greatest Common Factor in addtion and subtraction of fraction? Answered by Penny Nom. 





Which one has the most factors? 
20031031 

From Kristi: Of all the whole numbers less than or equal to 5000, which one has the most factors? Answered by Claude Tardif. 





1/x + 1/y = 5/12 
20031030 

From Ben: 1/x +1/y =5/12, what is the sum of x and y? Answered by Penny Nom. 





Relatively prime 
20030927 

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





Division names 
20030310 

From A parent: what is the answer to a division problem called Answered by Penny Nom. 





(n+17)(n+7) = 0 
20030305 

From Janea:
What is the answer to 1. (n+17)(n+7)=0 What is the answer to:2. (y15)(y100)=0 Answered by Penny Nom. 





Multiples of all four of the numbers 2, 3, 4, and 5 
20030211 

From Stephanie: How many of the first 1000 positive integers are multiples of all four of the numbers 2, 3, 4, and 5? Answered by Penny Nom. 





Some 5th grade problems 
20030124 

From Sabrina:
[What is the greatest common factor of 20,28, and 36?] next problem is [5k+7(k+8)= ] next problem [Curtis simplified 0.8 divided by 0.2 x 0.04 and got 10. Latoya Simplified and got 1.6. is either correct? Can you explaine how you got the answer please.] 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. 





For what divisors can you get a remainder of 8? 
20021113 

From David: When dividing a 3digit number by a 1digit number, for what divisors can you get a remainder of 8? Answered by Penny Nom. 





Reduce 79,537/3,623,420 
20011213 

From Eliana: How do you reduce 79,537/3,623,420. Answered by Claude Tardif. 





GCD and LCM 
20010924 

From David: Find the GCD adn LCM of the following numbers. Assume p 2 to the power p, 3 to power q, 5 to power r and 2 to power q, 3 to power r, 7 to power p Answered by Penny Nom. 





Greatest Common Factor 
20010509 

From Nicole: What is the Greatest Common Facter for:
126,261 1008,1080 546,1995 128,256 and 255,256 Answered by Penny Nom. 





Find the two numbers 
20010221 

From A grade 6 student: Find the two numbers: 5 is a common factor; 100 is a common multiple; neither number is a mulitple of the other; both are even. 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. 





Greatest common factor 
20010117 

From A teacher: I'm a teacher at a local Middle School and I would like the answers for the following questions. What is the greatest common factor for.. 546 and 780 156 and 732 . . . Answered by Leeanne Boehm and 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. 





Dividing with decimals 
20001115 

From Alex: I teach math and my class and I were discussing the dividing of decimals. I explained that if there is a decimal in the divisor, it needs to be moved and so does the decimal in the dividend. My question is why is it necessary to move the decimal point in the divisor before dividing? Answered by Penny Nom. 





Divisors of 2000 
20000606 

From Amanda Semi:
 find the product of all the divisors of 2000
 dog trainer time has 100m of fencing to enclose a rectangular exercise yard. One side of the yard can include all or part of one side of his building. iff the side of his building is 30 m, determine the maximum area he can enclose
Answered by Claude Tardif. 





Factors 
20000127 

From Pam: My son [age 9, 4th grade] has a math problem with factors. I need to know how to do the problem that involves the factor 24. I'm not even sure where to start. Answered by Harley Weston. 





Two algebra problems 
19991217 

From Michael Standfest: If x+4 is a factor of 2x^{4}+kx^{3}3kx^{2}+6x40, find k and Prove that n^{2}n is even for all n, using the proof of contradiction Answered by Penny Nom. 





An odd number of factors 
19991022 

From Melissa: What is the common name used for numbers that have an odd number of factors? What is the least positive integer that has exactly 13 factors? Answered by Penny Nom. 





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. 





Quotients 
19990225 

From Brian Healey: what is a quotient? what is a divisor? what is a divident? Answered by Jack LeSage.






Pick any odd number, square it, and then divide it by 8 
19981127 

From Brenda Meagher: Pick any odd number, square it, and then divide it by 8. No matter what odd number is chosen and squared and divided by 8, the remainder is one. Could you please explain this to me or is there a pattern that I am not aware Answered by Harley Weston. 





Composite Numbers 
19981007 

From Greg Murphy: What type of composite number has an odd number of factors? Answered by Harley Weston. 





Students and Lockers 
19981002 

From Mike: There is a row of 1000 lockers. There is a line of 1000 students. Student number 1 starts at the first locker and opens all 1000. Student number 2 starts at the second locker and closes every other one. Student number 3 starts at the third locker and goes to every third one, closing the open ones and opening the closed ones. Student number 4 does the same with every fourth locker and so on down the line... After all 1000 students have gone how many lockers are open and which ones are they? Please help! There is proboly a simple solution but we couldnt figure it out for the life of us. Please let us know how you solve it. Answered by Patrick Maidorn 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. 





A divisor. 
19980905 

From Kim Tangney: When 391 758 and 394 915 are divided by a certain three digit numbers, the three digit remainder is the same in each case. Find the divisor. 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. 





Greatest Common Factor. 
19980109 

From Percy Stribling: how do you figure out what the greater common factor is? Answered by Penny Nom. 





Number of factors 
19960130 

From Chrissy: What number has exactly 13 positive factors? Answered by Penny Nom. 





quel sont les plus grands diviseurs communs? 
20050907 

From Sylvain: quel sont les plus grands diviseurs communs? Answered by Claude Tardif. 

