See also the
Dr. Math FAQ:
learning to factor
3D and higher
Browse Middle School Factoring Numbers
Stars indicate particularly interesting answers or
good places to begin browsing.
Working with variables?
Try Middle School Factoring Expressions.
Selected answers to common questions:
Finding a least common denominator (LCD).
Table of factors 1-60.
- Are Negatives Factors of Other Numbers? [07/16/2003]
Are negative numbers factors of other numbers? Is -3 a factor of 3?
Is -3 a multiple of 3?
- Concept of Factoring [03/22/1997]
Could you explain the concept of factoring and give examples of its
- Factoring Factorials [05/24/1997]
If 30! is factored into primes, how many fives will the factorization
- Finding All the Factors of a Number [09/10/2001]
What are the factors of 1-100?
- Finding LCDs, LCMs, and GCFs [06/09/1998]
How do you find the greatest common factor, the least common multiple,
and the least common denominator?
- Finding the Factors of a Number [09/24/2001]
How can I find the factor of a number?
- Least Common Multiple Puzzle [03/24/2003]
What is the smallest number divisible by 1,2,3,4,5,6,8,9,10 that is
- Prime Factorization [1/26/1995]
Could you give me a crash course on prime factorization?
- Prime Factorization [01/22/1997]
How do you find the prime factorization of a number?
- Write Numbers as Products of Prime Factors [10/23/1996]
Write each of the following numbers as a product of its prime factors: 4,
6, 8, 10, 12, 14.
- 1005! / 10^n: A Number Puzzle [9/11/1996]
Find the largest positive integer, n, such that 1005! is divisible by 10
to the power of n.
- 24 Hours in a Day [08/15/2001]
Why divide the day into 24 equal parts? Why not 23 or 25?
- Cancelling Fractions [03/06/2002]
How do I cancel this problem: 1/5 x 40/1 x 1/2 ?
- Code with Only a String of 1's [10/28/2002]
You need to send a numeric code to someone, such as one used to
unlock a padlock.
- Counting the Number of Factors [01/04/1999]
Is there a systematic way to find the number less than 100 that has the
greatest number of factors?
- Decals on Lockers [02/28/2002]
The lockers in Pythagoras Middle School are numbered 1 through 500.
Starting the count with locker 1, every 6th locker has a blue decal, evey
9th locker has a yellow decal and every 10th locker has a green decal.
How many lockers have all 3 decals?
- Difference of Two Squares [09/04/2002]
I understand how to get the difference of two squares but how would
you get the equation when you have the answer?
- Divisibility by 3 in Three Consecutive Numbers [10/07/2002]
With any combination of consecutive natural numbers, why is one
integer divisible by three and why is ONLY one number divisible by 3?
- Divisibility Tests to Find the Smallest Prime Factor of a Number [02/02/2006]
How can I quickly find the smallest positive prime divisor of 1633
without having to do lots of divisions to check the possibilities?
- Division Quotient [11/06/2002]
In a division sentence, when will the quotient be odd? When will it
- Euclid's Algorithm for Finding a GCD [10/12/2002]
Find the only number besides one that is a common factor of 163231,
152057, and 135749.
- Explaining Greatest Common Factor [12/19/2005]
What does GCF mean? How do I figure it out?
- Factoring and Cancelling in Long Division [08/29/2003]
How do I perform long division? i.e. 1,002,240,000 / 86400
- Factoring and Divisibility Rules [12/18/1997]
I have no idea how to factor these problems: 12*13-60+12^2; 11^2-6*11+
- Factoring Completely and Efficiently [09/05/2014]
A student factors a number by starting to divide it by 1, then by 2, then 3, ... How
soon can she stop? Doctor Ian suggests prime factorization; Doctor Peterson shares
two insights from divisibility.
- Factoring Fractions [05/31/2001]
I am having a major problem trying to figure out how to add fractions
that have different denominators.
- Factoring in General [12/22/1995]
I have never figured out factoring. I can sort of do it but I don't
always get it right. Can you tell me how to factor better?
- Factoring Strategies [11/01/2002]
Find a number having 5 factors and a number having 13 factors and
explain your thinking and strategies.
- Factoring Very Large Numbers into Primes [12/05/2003]
Is there a way to factor really big numbers into primes other than the
usual method of dividing by successive primes?
- Factor Pairs [05/16/1999]
What is a factor pair?
- Factors and Rectangles [06/25/1998]
I'm trying to figure out what a rectangle and factors have in common.
- The Factors of Perfect Squares [04/26/2008]
Why are perfect squares the only numbers with an odd number of factors?
- Factors of Zero [10/21/2005]
What numbers are factors of zero? Since zero can be divided by any
number, are they all factors? Is zero itself a factor?
- Fermat's Factorization Method [01/29/1999]
Can you describe Fermat's method of factoring an integer?
- Finding Factor Pairs for Whole Numbers [11/29/2005]
What are factor pairs, and how do I find the factor pairs of a number
- Finding Integers Given LCM and GCD [11/05/2002]
The least common multiple of two positive integers is 144, and the
greatest common divisor is 2. Neither integer is 2. Find both
- Finding Least Common Multiple by Using Prime Factors [11/05/2003]
Can you explain how the prime factorization of a pair of numbers can help you find the least common multiple of those numbers?
- Finding Least Common Multiple for Day Problem [01/14/2004]
Club A meets every 7 days. Club B meets every 10 days. How often
will the clubs meet on the same day?
- Finding Least Common Multiple (LCM) by Factoring [10/19/2001]
Find the least common multiple of 6, 8, and 9: figure prime factors and
find the product of the greatest power of each prime factor.
- Finding the Greatest Common Factor of Two Different Numbers [01/06/1998]
Finding the GCF of two different numbers after using a factoring tree to
find their factors.