GCF Calculator

Calculate the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of two numbers.

GCF via Euclidean algorithm: gcd(a,b) = gcd(b, a mod b) until remainder = 0; LCM = (a x b) / GCF
GCF(48, 60) = 12 (largest common divisor); LCM(48, 60) = 240 (smallest common multiple)

What is the difference between GCF and LCM?

GCF (Greatest Common Factor) is the largest number that divides evenly into both numbers. LCM (Least Common Multiple) is the smallest number that both numbers divide into evenly. Example: 12 and 18 - GCF = 6 (largest divider), LCM = 36 (smallest shared multiple). Think: GCF goes INTO numbers, LCM numbers go INTO it. GCF <= smaller number, LCM >= larger number.

How do you find GCF manually?

Methods: 1) List factors, find largest common. Example: 24 (1,2,3,4,6,8,12,24) and 36 (1,2,3,4,6,9,12,18,36) -> GCF = 12. 2) Prime factorization: 24 = 2^3x3, 36 = 2^2x3^2 -> Common factors = 2^2x3 = 12. 3) Euclidean algorithm (what calculator uses): Divide, use remainder, repeat until 0. Fastest for large numbers.

When do you use GCF in real life?

Common uses: Simplifying fractions (24/36 / GCF(12) = 2/3), dividing items evenly (24 boys, 36 girls into equal groups = 12 groups), cutting materials to largest size (24" and 36" boards → 12" pieces), music rhythm patterns, gear ratios, tile/flooring layouts. Anytime you need to find largest common division.

What is the GCF of prime numbers?

GCF of two prime numbers is always 1 (they share no common factors except 1). Example: GCF(7, 11) = 1. Numbers with GCF = 1 are "relatively prime" or "coprime" even if they're not prime themselves. Example: 8 and 9 aren't prime, but GCF(8,9) = 1, so they're coprime. Prime numbers are always coprime with each other.