GCF Calculator (Greatest Common Factor)

Step 1: Enter two or more positive whole numbers separated by commas or spaces.

Step 2: Click Calculate to see the GCF.

Step 3: Review the step-by-step Euclidean algorithm and the prime factorization of each number.

The greatest common factor (GCF), also called greatest common divisor (GCD) or highest common factor (HCF), is the largest positive integer that divides every number in a set without leaving a remainder.

For example, the GCF of 12 and 18 is 6 — both numbers divide evenly by 6, and no larger integer works.

The GCF is used to reduce fractions to lowest terms, simplify ratios, and solve divisibility problems in number theory.

Euclidean algorithm: GCF(a, b) = GCF(b, a mod b), repeating until the remainder is 0.

Example: GCF(48, 18)
48 ÷ 18 = 2 remainder 12
18 ÷ 12 = 1 remainder 6
12 ÷ 6 = 2 remainder 0 → GCF = 6

For three or more numbers: GCF(a, b, c) = GCF(GCF(a, b), c)

Example 1: GCF(48, 60) = 12 — useful for reducing 48/60 to 4/5.

Example 2: GCF(17, 23) = 1 — both are prime, so they share no common factor besides 1.

Example 3: GCF(100, 250, 400) = 50 — the largest number that divides all three.

GCF of 1 means coprime. Numbers share no factors except 1.

Prime factorization method — multiply the lowest power of each shared prime.

Always simplifies fractions. Divide numerator and denominator by their GCF.

For negatives, take absolute values — GCF is always positive.