GCF Calculator

Q: What is the GCF?

The Greatest Common Factor (GCF) is the largest number that divides two or more numbers evenly. Example: GCF(12, 18) = 6 because 6 is the largest number that divides both 12 and 18.

Q: How do I find the GCF?

Use the Euclidean algorithm: repeatedly divide the larger by the smaller until the remainder is 0. The last non-zero remainder is the GCF.

Q: What is the difference between GCF and LCM?

GCF is the largest common factor (divides both). LCM is the smallest common multiple (both divide into). Relationship: GCF × LCM = a × b.

Q: What does it mean if GCF = 1?

If GCF(a, b) = 1, the numbers are coprime (relatively prime) — they share no common factors other than 1. Example: GCF(8, 15) = 1.

Find the Greatest Common Factor (GCF) of any two numbers. See the Euclidean algorithm, prime factorization, and complete factor lists with visual Venn diagram.

📐 GCF Calculator

Result

Visual Diagram

Definition

What is GCF Calculator?

A GCF Calculator (Greatest Common Factor) finds the largest number that divides two or more numbers without leaving a remainder. The GCF is also called the GCD (Greatest Common Divisor) or HCF (Highest Common Factor).

The GCF is the foundation of fraction simplification. To simplify a fraction, divide both the numerator and denominator by their GCF. The GCF is also used in solving algebraic equations, factoring polynomials, and optimizing ratios.

The most efficient method for finding the GCF is the Euclidean algorithm, which uses repeated division to find the GCF in O(log n) time.

Interactive Visualization

Formula

GCF Calculator Formula

Euclidean Algorithm:

Divide the larger number by the smaller
If the remainder is 0, the divisor is the GCF
Otherwise, replace the larger number with the smaller, and the smaller with the remainder
Repeat until the remainder is 0

Example: GCF(48, 18)

48 ÷ 18 = 2 R 12 → 18 ÷ 12 = 1 R 6 → 12 ÷ 6 = 2 R 0 → GCF = 6

Examples

Worked Examples

GCF(12, 8)

12 ÷ 8 = 1 R 4 → 8 ÷ 4 = 2 R 0 → GCF = 4.

GCF(36, 24)

36 ÷ 24 = 1 R 12 → 24 ÷ 12 = 2 R 0 → GCF = 12.

GCF(17, 13)

17 ÷ 13 = 1 R 4 → 13 ÷ 4 = 3 R 1 → 4 ÷ 1 = 4 R 0 → GCF = 1 (coprime).

GCF(100, 75)

100 ÷ 75 = 1 R 25 → 75 ÷ 25 = 3 R 0 → GCF = 25.

FAQ

Frequently Asked Questions

Common questions about the gcf calculator.

What is the GCF?

The Greatest Common Factor (GCF) is the largest number that divides two or more numbers evenly. Example: GCF(12, 18) = 6 because 6 is the largest number that divides both 12 and 18.

How do I find the GCF?

Use the Euclidean algorithm: repeatedly divide the larger by the smaller until the remainder is 0. The last non-zero remainder is the GCF.

What is the difference between GCF and LCM?

GCF is the largest common factor (divides both). LCM is the smallest common multiple (both divide into). Relationship: GCF × LCM = a × b.

What does it mean if GCF = 1?

If GCF(a, b) = 1, the numbers are coprime (relatively prime) — they share no common factors other than 1. Example: GCF(8, 15) = 1.

How is GCF used to simplify fractions?

Divide both the numerator and denominator by the GCF. Example: 24/36 → GCF(24,36) = 12 → 24÷12 / 36÷12 = 2/3.