GCF Calculator
Find the Greatest Common Factor (GCF) of two or more numbers. Also known as Greatest Common Divisor (GCD) or Highest Common Factor (HCF).
Greatest Common Factor
—
What is the Greatest Common Factor?
The Greatest Common Factor (GCF) of two or more integers is the largest positive integer that divides each of the numbers without a remainder. It is also called the Greatest Common Divisor (GCD) or Highest Common Factor (HCF).
Methods to Find GCF
Method 1 — Prime Factorization
Break each number into its prime factors, then multiply the common ones.
GCF(48, 36):
48 = 2 × 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
Common factors: 2 × 2 × 3 = 12
48 = 2 × 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
Common factors: 2 × 2 × 3 = 12
Method 2 — Euclidean Algorithm
GCF(a, b) = GCF(b, a mod b) until remainder = 0
GCF(48, 36):
GCF(48, 36) → GCF(36, 12) → GCF(12, 0) = 12
GCF(48, 36) → GCF(36, 12) → GCF(12, 0) = 12
GCF Reference Table
| Numbers | GCF |
|---|---|
| 12, 18 | 6 |
| 24, 36 | 12 |
| 15, 25 | 5 |
| 100, 75 | 25 |
| 56, 98 | 14 |
| 120, 180 | 60 |
FAQ
What is GCF used for?
GCF is used to simplify fractions, factor polynomials, and solve problems involving groups or equal sharing.
What is the GCF of two prime numbers?
The GCF of any two distinct prime numbers is always 1, because primes have no common factors other than 1.
Related Calculators
Last updated: 2026-08-08