Factor Calculator

GCF Calculator

Find GCF (or GCD) for two numbers and see the exact steps taken by the Euclidean division algorithm.

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What is the Greatest Common Factor?

The Greatest Common Factor (GCF) is the largest positive integer that divides 2 or more numbers without a remainder. The GCF of 48 and 60 is 12 because 12 is the biggest number that divides both 48 and 60 evenly. The GCF is also called the Greatest Common Divisor (GCD) or Highest Common Factor (HCF).

The GCF calculator above uses the Euclidean algorithm, a method discovered by the Greek mathematician Euclid around 300 BCE. The Euclidean algorithm finds the GCF through repeated division — divide the larger number by the smaller, then divide the smaller by the remainder, and repeat until the remainder reaches 0. The last non-zero remainder is the GCF.

3 Methods to Find GCF

Select a number pair to watch the Euclidean algorithm solve for the GCF step by step.

Euclidean Algorithm Walkthrough

Step 1:60 = 48 × 1 + 12
Step 2:48 = 12 × 4 + 0
GCF(48, 60) = 12

Method 1: Listing Factors

List all factors of each number, identify the common ones, and pick the largest.

Method 2: Euclidean Algorithm

Repeated division until remainder = 0. Fastest for large numbers.

Method 3: Prime Factorization

Find prime factorizations, take common primes at lowest exponents, multiply.

GCF Worked Examples

GCF(24, 36)= 12

24 = 2³ × 3, 36 = 2² × 3². Shared primes at lowest exponents: 2² × 3 = 12.

GCF(48, 60)= 12
GCF(72, 108)= 36
GCF(150, 225)= 75

Frequently Asked Questions

GCF (Greatest Common Factor) and GCD (Greatest Common Divisor) are 2 names for the same value. GCF is more common in elementary education and the United States curriculum. GCD is standard in university mathematics and international usage. Both refer to the largest positive integer that divides 2 or more numbers without remainder. The GCF of 24 and 36 is 12, and the GCD of 24 and 36 is also 12.