Greatest common factor

The greatest common factor (GCF) of two numbers is the largest number that divides both exactly. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24; the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The factors they share are 1, 2, 3, 4, 6, 12, and the greatest of those is 12.

The GCF is the biggest number that fits into both. Pulling it out front of a sum is the distributive property in reverse: 24 + 36 = 12 × (2 + 3).