GCF Calculator
Find the Greatest Common Factor (GCF), LCM, or simplified ratio of any list of integers.
Numbers
Updates as you type
What to solve for
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Greatest Common Factor — the largest integer that divides every input evenly.
Quick examples (click to load)
Numbers
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1
2
Paste a list of numbers
Separate numbers with commas, spaces, or new lines. We’ll keep the first 10 valid positive integers.
Method 1 — Factor ladder
Divide by shared primes until no prime divides all inputs| Set numbers above to see the ladder. |
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Multiply the divisors on the left to get the GCF. The bottom row shows what remains (mutually coprime).
Method 2 — Euclidean algorithm
GCF(a, b) = GCF(b, a mod b), repeat until remainder is 0- Set numbers above to see the running pairwise calculation.
Verification
Each input should be an exact multiple of the GCF- Set numbers above to see the verification.
Formula
GCF(a, b)
=
GCF(b, a mod b)
- GCF
- Greatest common factor (also called HCF, GCD) — the largest integer that divides every input evenly.
- LCM
- Least common multiple — the smallest positive integer every input divides into. For two numbers: LCM = |a × b| / GCF.
- Coprime
- A set whose GCF is 1. No prime divides every input, so the ratio is already in lowest terms.
Euclidean algorithm — your numbers
- Inputs: —
- Shared prime factors: —
- Simplified ratio: —
- GCF = —
For more than two numbers, apply the identity pairwise: GCF(a, b, c) = GCF(GCF(a, b), c). The factor-ladder view above runs this in parallel — every step divides the whole row by a single shared prime.