The greatest common factor is the largest number that divides each input exactly. It is used to simplify fractions and split items into equal groups.
How to use the GCF Calculator
- First number
- Second number
- Third number (optional, 0 to skip)
Results update as you type, and every field accepts the units shown in its menu.
How it works
Euclid’s algorithm repeatedly replaces the larger number with the remainder of dividing it by the smaller one.
Inputs explained
| Field | What to enter |
|---|---|
| First number | A number |
| Second number | A number |
| Third number (optional, 0 to skip) | A number |
Formula
gcd(a, b) = gcd(b, a mod b), until the remainder is 0Worked example
Inputs — First number: 84; Second number: 126; Third number (optional, 0 to skip): 210.
Results — Greatest common factor = 42; LCM of first two = 252.
Key terms
- Divisor
- A number that divides another exactly.
Frequently asked questions
What if the GCF is 1?
The numbers are relatively prime.
Does it work with decimals?
No, inputs are rounded to whole numbers.
What formula does the GCF Calculator use?
gcd(a, b) = gcd(b, a mod b), until the remainder is 0.