Greatest Common Factors and Least Common Multiples

I vaguely remember when I learned about factor trees and prime factorization for the first time, but they are definately important to finding the Greatest Common Factor (GCF) and the Least Common Multiple (LCM).  Though there is only one prime factorization of a number, there are 3 method for finding the prime factorization.
Remember a prime number has only 2 factors!
One method is increasing primes.  In this method you divide the number by increasing prime numbers.
Example:  84=2•2•3•7
               84÷2=42       42÷2=21      21÷3=7

There is the 2 factors method, where you keep writing numbers as a product of 2 factors.
Example:  84= 2•42
                       2•6•7
                       2•2•3•7
Then there is the factor tree, my favorite method.

Image from:  schoolworkout.co.uk

Above is an example of a factor tree for the number 72.  72 is broken down into 2 factors, 9 and 8, then 9 and 8 are broken down into 2 factors, and so on, until the numbers that are left are the prime numbers.  The numbers that are circled are the prime numbers. 

Once you understand prime factorization you can explore GCF and LCM.

GCF

GCF(a,b)= the largest number that is a factor of both a and b

Example:  GCF(7,14)=7

LCM

LCM(a,b)= the smallest number that is a multiple of both a and b

Example:  LCM(3,5)=15

Check out methods for finding the GCF and LCM at http://www.purplemath.com/modules/lcm_gcf.htm

Then you can test out your skills at http://www.math-play.com/Factors-and-Multiples-Jeopardy/Factors-and-Multiples-Jeopardy.html