GCF Calculator

GCF Calculator

Find the greatest common factor of two or more positive integers.

Last updated: June 2026 | By Patchworkr Team

Multiple Number Analysis
Number 1
Number 2
Number 3
Enter positive integers only. Invalid inputs are shown explicitly instead of being ignored.
Result
GCF
12
24, 36, 48 to GCF 12
Common factors: 1, 2, 3, 4, 6, 12

What GCF means

The greatest common factor is the largest positive integer that divides every input evenly.

Common factors

The common factors are every positive integer that divides all numbers in the list.

Formula and example

GCF(a, b, c, ...) = gcd(gcd(a, b), c, ...)

Example: 48, 64, and 80 have GCF 16.

Worked Example

Find the GCF of 48, 64, and 80.

1. Factor 48 = 2^4 x 3

2. Factor 64 = 2^6

3. Factor 80 = 2^4 x 5

4. Common factor = 2^4

Final answer: GCF 16

Frequently Asked Questions

Can I enter more than two numbers?

Yes. The calculator can analyze any length list of positive integers.

Why reject zero and negatives?

This version is focused on positive integers, so invalid inputs are rejected explicitly.

What if there is no common factor besides 1?

Then the GCF is 1, which is still a valid and useful result.

Does order matter?

No. GCF does not depend on the order of the numbers.

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