GCF Calculator - Greatest Common Factor

GCF Calculator — quick guide

1) Core idea

The greatest common factor (GCF, aka GCD) is the largest positive integer that divides all given numbers with zero remainder. It’s used to simplify fractions, group items evenly, and find common measures.

2) How this tool works

• Two numbers: uses the Euclidean algorithm (repeat a % b until remainder = 0).
• Many numbers: reduces pairwise, i.e., GCF(a,b,c) = GCF(GCF(a,b), c).
• Extras shown: prime factorization and full factor lists for learning/verification.

3) Sanity checks

• GCF ≤ min(all inputs).
• If numbers are coprime, GCF = 1.
• The identity GCF(a,b) × LCM(a,b) = a × b holds (for two numbers).

4) Shortcuts that help

• If both numbers are even, GCF ≥ 2 (keep halving while both stay even).
• If one number divides the other, GCF is the smaller number.
• Use small primes first (2, 3, 5) to spot common factors quickly.

5) Common pitfalls

• Mixing up GCF and LCM (GCF is ≤ smallest input; LCM is ≥ largest input).
• Using highest (not lowest) prime powers for GCF in factorization.
• Entering non-positive or non-integer values (this tool expects positive integers).

6) Micro‑examples

• GCF(48, 18) = 6 (48 = 18×2 + 12; 18 = 12×1 + 6; 12 = 6×2 + 0).
• GCF(24, 36, 48) = 12.
• GCF(7, 11) = 1 (coprime).

7) Mini‑FAQ

• GCF vs LCM? GCF is the greatest shared divisor; LCM is the least shared multiple.
• Can negatives appear? Mathematically, GCF is non‑negative and sign doesn’t matter; this tool uses positive integers.
• What about zero? Conventionally, GCF(a, 0) = |a|, but zero is not accepted as input here.

8) Action tip

Enter numbers separated by commas to find a multi‑number GCF fast, then use it to simplify any related fractions in one step.