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Dr. Math FAQ:
learning to factor
3D and higher
Browse Middle School Factoring Numbers
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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?
- All in a Row: Divisible Except for One Consecutive Pair [02/17/2015]
A twelve year-old struggles to make sense of a word problem in which students relate
their ordinal positions to the divisibility of one common number. Doctor Greenie
outlines one way to proceed methodically through the clues.
- 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?
- Deducing Dimensions without Algebra, with Area and Perimeter: Which Clue First? [10/21/2017]
Given its perimeter and area, a teen struggles to use the former to determine a
rectangle's dimensions without algebra. Doctor Ian breaks it down a different way;
emphasizing strategic problem-solving throughout, he shares a more effective
- 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?