## Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) of two non-zero integers is the largest positive integer that divides both numbers without remainder.

Example #1:

GCF(6, 18) = ?

Factors of 6: 1, 2, 3, 6

Factors of 18: 1, 2, 3, 6, 18

The largest factor common to both numbers is 6

∴ GCF(6, 18) = 6

GCF(18, −4) = ?

Solution #1:

Factors of 6: 1, 2, 3, 6

Factors of 18: 1, 2, 3, 6, 18

The largest factor common to both numbers is 6

∴ GCF(6, 18) = 6

Example #2:

GCF(18, −4) = ?

Solution #2:

(The negative number sign may be ignored as divisibility is not affected)

Factors of 18:
1, 2, 3, 6, 18

Factors of 4: 1, 2, 4

The largest factor common to both numbers is 2

∴ GCF(18, −4) = 2

Factors of 4: 1, 2, 4

The largest factor common to both numbers is 2

∴ GCF(18, −4) = 2

Properties: