Definition
Greatest common factor
The greatest common factor is the largest positive whole number that divides every given whole number exactly.
What it means
Write the factors of each number, then look only at the factors the lists share. The greatest common factor is the biggest number left. You can use it to make equal groups as large as possible or to simplify a fraction.
Remember it
Find the shared factors, then choose the biggest one.
Example
For 20 and 30, the common factors are 1, 2, 5, and 10. The biggest is 10, so the greatest common factor of 20 and 30 is 10.
Watch for
15 is not a common factor of 20 and 30 because 15 does not divide 20 exactly.
Common mix-up
A greatest common factor is a factor, so it cannot be larger than the smallest number in the set.
Exact meaning
For two or more positive whole numbers, the greatest common factor is the largest positive whole number that is a factor of every number in the set. It is also called the highest common factor or greatest common divisor.