What is the greatest common factor (GCF) in math?
The greatest common factor of two or more numbers is the greatest whole number that divides evenly into all these numbers.
Two Methods to Find GFC
1  Method that may be used for small numbers
Examples: Find greatest common factor of the numbers 12 and 18.
1) List all the factors of 12 which are: 1, 2, 3 , 4, 6, 12
2) List all the factors of 18 which are: 1, 2, 3 , 6, 9, 18
Look for the common factors of 12 and 18: 1, 2, 3, and 6.
The greatest of the common factor (GCF) of 12 and 18 is 6.
2  Method that may be used for all numbers including large numbers
Examples: Find greatest common factor of the numbers 60 and 90.
1) The prime factorization of 60 is: 60 = 2^{ 2}×3×5 = 2×2×3×5
2) The prime factorization of 90 is: 90 = 2 × 3^{ 2}×5 = 2×3×3×5
Look for the common factors of 60 and 90 in the prime factorization: 2, 3, and 5.
The greatest common factor (GCF) of 60 and 90 is 2×3×5 = 30.
A
Greatest Factor Calculator (GCF) may be used to check your answers.
Answer the following questions
(Solutions and explanations are included)

Find the greatest common factor of 36 and 42.

Find the greatest common factor of 45, 60 and 75.

What is the greatest common factor of 360 and 252?

What is the greatest common factor of 324, 666 and 756?

a) Find the GCF of 12 and 16.
b) Use the result in part a) to find the GCF of 1200 and 1600.
