Greatest Common Factor (GCF)

In general, the greatest common factor (gcf) is the largest factor that a set of terms have in common.

Example 1: 6x³ is the greatest common factor of 12x⁷ and 18x³.

Example 2: 6x³y² is the greatest common factor of 12x⁵y²z, 6x⁴y³z and 18x³y⁴.

Example 3: 2xy is a common factor of 12x⁵y²z, 6x⁴y³z and 18x³y⁴, but it is NOT the GREATEST common factor.

Example 4: 6x⁵ is NOT a COMMON factor of 12x⁵y²z, 6x⁴y³z and 18x³y⁴. It is therefore not the GREATEST common factor.

Example 5: 6x¹⁰ is NOT a factor of 12x⁵y²z, 6x⁴y³z or 18x³y⁴. It is therefore not the greatest common factor.

Definition (Natural Numbers)

In terms of numbers, the greatest common factor (gcf) is the largest natural number that exactly divides two or more given natural numbers.

Example 1: 6 is the greatest common factor of 12 and 18.

Example 2: 2 is a common factor of 12 and 18, but it is NOT the GREATEST common factor.

Example 3: 4 is NOT a COMMON factor of 12 and 18. It is therefore not the GREATEST common factor.

Example 4: 8 is NOT a factor of 12 or 18. It is therefore not the greatest common factor.