GCF calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- Euclid's method: repeatedly replace the larger number by the remainder after division.
- 48 = 0 × 180 + 48
- 180 = 3 × 48 + 36
- 48 = 1 × 36 + 12
- 36 = 3 × 12 + 0
- 12 = 0 × 72 + 12
- 72 = 6 × 12 + 0
- The greatest common factor is 12.
| Inputs | Answer |
|---|---|
| Whole numbers: 48, 180, 72 | The GCF of 48, 180, 72 is 12. |
| Whole numbers: 24, 36 | The GCF of 24, 36 is 12. |
| Whole numbers: 17, 31 | The GCF of 17, 31 is 1. |
How to use it
The greatest common factor (GCF, also called the greatest common divisor) is the largest whole number that divides all of the numbers exactly. The calculator uses Euclid's method: replace the larger number by the remainder after dividing by the smaller one until the remainder is 0; the last non-zero value is the GCF.
The GCF is what you divide by to simplify a fraction. The LCM of the same numbers is shown as well.
Frequently asked questions
What is the GCF of 48 and 180?
12, since 12 divides both and no larger number does.
How is the GCF used?
To simplify fractions and to split things into the largest equal groups.
What if the GCF is 1?
The numbers are called coprime (relatively prime).
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.