the greatest factor that divides two numbers. to find the gcf, list the prime factors of each number, circle the pairs of factors both numbers have in common, and multiply those factors together.
example: the gcf of 12 (2 × 2 × 3) and 30 (2 × 3 × 5) is 6 (2 x 3). to check, make sure both 12 and 30 divide by 6.