Greatest Common Factor (GCF) Calculator

How to Find the Greatest Common Factor

The Greatest Common Factor (GCF) of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder.

Method 1: Euclidean Algorithm (used above)

1. Divide the larger number by the smaller. Note the remainder.
2. Replace the pair (larger, smaller) with (smaller, remainder).
3. Repeat until the remainder is 0. The last non-zero divisor is the GCF.

Method 2: Listing Factors

1. List all factors of each number
2. Identify the factors that appear in all lists (common factors)
3. Select the largest common factor — this is the GCF

Method 3: Prime Factorization

1. Find the prime factorization of each number
2. Identify which prime factors appear in all factorizations
3. For each common prime factor, take the lowest exponent
4. Multiply these prime factors raised to their lowest exponents

GCF = product of (common prime factors)^{lowest exponent}

Example: GCF(12, 18) using prime factorization

• 12 = 2² × 3¹
• 18 = 2¹ × 3²
• Common primes: 2 and 3 — take the lowest exponent of each
• GCF = 2¹ × 3¹ = 6

Related Calculators

• Least Common Multiple (LCM) Calculator
• Prime Factorization Calculator
• Divisors of a Number
• Multiples of a Number
• Fraction Calculator
• Fraction Simplifier (uses GCF to reduce fractions)