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divisors

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Two problems 2010-05-27
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 six-digit 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 2010-04-27
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 2010-01-06
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 2010-01-05
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.
How many students were there 2009-01-25
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 2009-01-06
From Madison:
what are the factors of 878
Answered by Robert Dawson.
Do all square numbers have an odd number or factors? 2008-12-11
From Amy:
Do all square numbers have an odd number or factors?
Answered by Victoria West.
A remainder of 8 2008-10-23
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 2008-09-18
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 2008-07-20
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? 2008-06-27
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. 2008-06-24
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? 2008-02-26
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 2007-11-26
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? 2007-09-13
From Miska:
What are the factors of 111?
Answered by Penny Nom.
How many stairs in the flight are stepped on exactly once? 2007-09-03
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 2007-06-27
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.
Find the divisors 2006-08-21
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.
When 391758 and 394915 are divided by a certain three digit number, ... 2006-07-26
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+2x-3 is a factor f(x)=x^4+2x^3-7x^2+ax+b 2006-04-06
From Maha:
Given that x2+2x-3 is a factor f(x)=x4+2x3-7x2+ax+b, find a and b and hence factor f(x) completely.
Answered by Penny Nom.
given that p is a prime and p|a^n, prove that p^n|a^n 2006-03-24
From Janna:
given that p is a prime and p|an, prove that pn|an
Answered by Stephen La Rocque.
How many divisors does the number 138600 have? 2006-02-08
From Joe:
How many divisors does the number 138600 have?
Answered by Steve La Rocque and Penny Nom.
For what divisors can you get a remainder of 8? 2006-01-06
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 2005-11-23
From Mary Lou:
Show the 10 numbers with exactly 5 divisors.
Answered by Penny Nom.
n^2+n-1 has no divisors ending with 3 or 7 2005-09-08
From Arne:
at least it seems like for any integers n and k,
10k+3 and 10k+7 do not divide nē+n-1
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.
Some numbers less than 100 2004-09-17
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 2004-09-14
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 tic-marks on a number line).
Answered by Harley Weston.
an integer with three factors 2004-08-03
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 2004-06-02
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? 2003-11-09
From Mary:
What is a number that has exactly 13 factors?
Answered by Penny Nom.
Which one has the most factors? 2003-10-31
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 2003-10-30
From Ben:
1/x +1/y =5/12, what is the sum of x and y?
Answered by Penny Nom.
Relatively prime 2003-09-27
From James:
what is the definition a relative prime numbers?
Answered by Penny Nom.
Division names 2003-03-10
From A parent:
what is the answer to a division problem called
Answered by Penny Nom.
(n+17)(n+7) = 0 2003-03-05
From Janea:

What is the answer to 1. (n+17)(n+7)=0

What is the answer to:2. (y-15)(y-100)=0


Answered by Penny Nom.
Multiples of all four of the numbers 2, 3, 4, and 5 2003-02-11
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.
Composites, primes, factors and common factors 2002-11-20
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.
Find the two numbers 2001-02-21
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? 2001-01-23
From John:
What number from 1 to 25 has the most factors?
Answered by Penny Nom.
A pair of numbers whose GCF is 28 2000-12-27
From John:
Name 2 different pairs of numbers whose GCF is 28.
Answered by Penny Nom.
Dividing with decimals 2000-11-15
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 2000-06-06
From Amanda Semi :
  1. find the product of all the divisors of 2000
  2. 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 2000-01-27
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 1999-12-17
From Michael Standfest:
If x+4 is a factor of 2x4+kx3-3kx2+6x-40, find k

and

Prove that n2-n is even for all n, using the proof of contradiction
Answered by Penny Nom.

An odd number of factors 1999-10-22
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.
T-shirts 1999-04-04
From Valerie:
At a discount T-shirt shop the manager marked a special batch of T-shirts 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.

Pick any odd number, square it, and then divide it by 8 1998-11-27
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 1998-10-07
From Greg Murphy:
What type of composite number has an odd number of factors?
Answered by Harley Weston.
Students and Lockers 1998-10-02
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 1998-09-19
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. 1998-09-05
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 1998-01-26
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.
Number of factors 1996-01-30
From Chrissy:
What number has exactly 13 positive factors?
Answered by Penny Nom.
 
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