GCF Calculator
Euclidean algorithm on a list of whole numbers. Click any i for detail.
Integers
Numbers
i
List
Two or more positive integers, commas or spaces. |
|---|
How to use this calculator
- Enter two or more positive integers separated by commas or spaces.
- Read the greatest common factor (GCD).
- Use the pairwise LCM hint when shown for the first two numbers.
- Reduce fractions by dividing top and bottom by the GCF.
Results explained
The GCF is the largest integer dividing every input evenly. The Euclidean algorithm finds it without factoring completely.
Quick reference: GCF
gcf(48, 18) = 6 because 6 is the largest shared divisor.
| Item | Detail |
|---|---|
| Alias | GCD means the same thing here |
| Euclid step | gcd(a,b) = gcd(b, a mod b) |
| Reduce 48/18 | divide by 6 → 8/3 |
| List of three+ | fold gcd across the list |
Decimals are rounded to integers before gcd runs.
How the estimate is built
gcd(a,b) via Euclidean algorithm; gcd(a,b,c) = gcd(gcd(a,b), c).
Example scenario
48, 18, 30 → 6.
FAQ
How is GCF different from LCM?
GCF is the largest shared factor. LCM is the smallest common multiple.
What about negative inputs?
Absolute values are used; gcd is defined on positive integers here.
Can I use this to simplify fractions?
Yes. Divide numerator and denominator by gcf(numerator, denominator).