Greatest Common Factor (GCF)

The greatest common factor of a set of numbers such as a and b is the largest positive integer that divides both a and b. The GCF can be thought of like the inverse of LCM.

GCF(a, b) * LCM(a, b) = a * b

To find the GCF of a set of numbers:

• List the prime factors of each number
• Multiply the factors that all numbers have in common
• If there are no common prime factors, then the GCF is 1.

Example: What is the Greatest Common Factor (GCF) of 42, 56 and 84?

• 42 = 2 * 3 * 7, 56 = 2³ * 7, 84 = 2² * 3 * 7
• The common prime factors among the set of numbers are: 2 and 7
• 2 * 7 = 14. GCF(42, 56, 84) = 14.