Greatest Common Factor Calculator
Adjust the inputs below. Results update as you type.
How it works
GCF (also called GCD) is the largest integer that divides all given numbers with no remainder. Euclidean algorithm: GCF(a,b) = GCF(b, a mod b) until remainder = 0. Example: GCF(48,18) → GCF(18,12) → GCF(12,6) → GCF(6,0) = 6. Used to simplify fractions (divide numerator and denominator by GCF) and solve word problems involving equal groups.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
The GCF is the largest number that divides all values evenly. Find it via the Euclidean algorithm or by multiplying the shared prime factors.
Worked example
GCF(12, 18): shared factors are 2 and 3, so GCF = 6.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
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Frequently asked questions
What is the greatest common factor?+
The largest integer that divides two or more numbers without a remainder — also called the greatest common divisor.
What is the Euclidean algorithm?+
A fast method: replace the larger number with its remainder when divided by the smaller, repeating until one becomes zero; the other is the GCF.
Why is the GCF useful?+
It simplifies fractions to lowest terms and helps factor expressions and solve ratio problems.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.