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Dr. Math FAQ:
learning to factor
3D and higher
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Selected answers to common questions:
Finding a least common denominator (LCD).
Table of factors 1-60.
- 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.
- Finding Two Numbers with Known Product and Difference [08/06/2008]
Two numbers have a product of 6800 and a difference of 5. Find the
numbers. How can I solve this without using algebra?
- Find Pairs of Positive Integers [10/15/2001]
Find pairs of positive integers whose greatest common factor is 1 and
whose sum is 2000.
- Find the Smallest Number... [10/21/1997]
... that has factors of 1, 2, 3, 4, 5, 6, 7, and 8.
- Five to the Third Power [09/20/2001]
What is 5 to the 3rd power? I put 15. Wrong!
- Formula for Greatest Common Divisor [01/08/1997]
Is there a formula to get the greatest common factor?
- Greatest Common Factor [06/02/1999]
Given their GCF, how can I find an even and an odd number such that one
is not a multiple of the other?
- Great Explanation of How to Find the Least Common Multiple [10/24/2007]
One alarm clock rings every 25 minutes, another every 30 minutes, and
another every 35 minutes. How long will it take for all three clocks
to ring at the same time?
- Help with Factoring [4/14/1996]
I've just started and can't figure out a logical way to get the hang of
- How Many Factor Pairs Does a Given Number Have? [03/19/2004]
I'm wondering if there is a formula or algorithm that will tell me
exactly how many pairs of factors a number has?
- How Many Pads of Paper? [10/30/2001]
A merchant marked some pads of paper down from $2.00 and sold the entire
lot. If the gross profit from the sale was $603.77, how many pads did he
- How to Find the Prime Factorization of a Whole Number [11/29/2005]
I'm really confused about how to find the prime factorization of a
number. Can you help me?
- Impossible Word [04/14/2001]
What word comes out to 575,151 when you multiply together the values of
- Integer Divisors [04/11/1997]
N has six distinct integer divisors including 1 and N. The product of
five of these is 648; find another divisor of N.
- Investigating Prime Factors as a Classroom Activity [06/27/2004]
If n is a composite number, is it true that all prime factors of n
must not exceed the square root of n?
- Laps and Least Common Multiples [05/24/2002]
Three people are running around a track at different speeds. When
will they all return to the starting point at the same time?
- Layers of Least Common Multiples [10/13/2012]
How does the "upside-down birthday cake method" work? Doctor Ian unpacks this
method for determining least common multiples, and compares it with conventional
- LCM 120, HCF 4 [01/24/2002]
Find three examples of two numbers if their LCM is 120 and their HCF is
- LCM among Decimals [06/09/2010]
Given two numbers not integers, an adult wonders how to determine their
least common multiple — or even their greatest common divisor.
Doctor Peterson shows how to extend the usual method by shifting
decimal places, and then un-shifting them.
- LCM and GCF, Combined: Why and How [12/20/2010]
A student familiar with simultaneously calculating the least common multiple (LCM) and
greatest common factor (GCF), as shared on Ask Dr. Math, re-visits the all-in-one
method. Doctor Peterson expands on his earlier explanation of the technique, then
extends it to apply to three numbers.
- Least Common Multiple [09/29/2001]
What is the least common multiple of 11, 13, and 17?
- Least Common Multiple, 2-10 [10/28/2002]
Find the smallest counting number that is divisible by the numbers 2
- Least Common Multiple Word Problem [12/10/1996]
Each of three businesses receives different sized cartons of glasses. If
all three receive the same number of glasses and none of them receive
more than a thousand glasses, how many glasses and cartons are in each
- Making a Factor Tree [03/26/1998]
How do you make a factor tree?
- Mental Math [07/25/2003]
I would like to find a trick for multiplying by 3367.
- Multiples and Factors [06/02/2003]
What is the difference between multiples and factors?
- Multiplicand, Multiplier [07/05/2001]
Do you agree with me that in the following mathematical sentence: 456x10,
456 is called the multiplicand and 10 is called the multiplier?
- Multiplying Fractions [02/06/2001]
I need help solving 8/9 * 3/5. What is cross-cancelling?
- Numbers with 5 Factors [02/06/2002]
I know that 16 has 5 factors (1,2,4,8,16). What other two numbers might
have 5 factors?
- One Approach to Finding LCM and GCF at the Same Time [03/02/2006]
I just learned a way of using a chart that lets you find the LCM and
the GCF for two numbers at the same time, quickly and easily. Here it is!
- One Billion as Product of Two Numbers with No Zeros [12/12/2001]
Write 1,000,000,000 as the product of two numbers, neither of which
contains any zeros.
- Precise Numbers [10/18/2001]
A precise number occurs when its proper divisors multiplied together
equal the number: 6 is a precise number because 1*2*3 = 6. Is there
another name or formula?
- Prime Factoring Large Numbers [03/28/2003]
What are the prime factors of 5515596313?
- Prime Factorization [01/07/1997]
How do you find the prime factorization of a number?
- Prime Factor Puzzle [10/24/2003]
The two prime factors of a number are greater than 12 but less than
25. The number is greater than 300 but less than 400. What is the
number? What are the factors?
- Prime Factors [01/28/2006]
What is a number with only two prime factors and no repeated factors?
- Prime Factors as Bricks [10/26/2001]
Is there another way to find prime factors besides making a factor tree?
- Prime Factors of 4,194,305 [09/20/1999]
How can I find the prime factors of 2^22+1?
- Prime Number Puzzle [09/27/2001]
I am the product of four primes, and the sum of these numbers is thirty.
My three digits are prime and different. What number am I?
- Prime Numbers vs. Prime Factors [01/13/1997]
What is the difference between a prime number and a prime factor?