Greatest Common Factor Calculator

Find the largest integer that divides every number in a list — simplifying fractions and ratios — not the smallest shared multiple.

How to use

Paste at least two integers, separated by spaces, commas or new lines.
Read the greatest common factor. gcd(48, 18) is 6; gcd(12, 18, 30) is 6.
Use that 6 to simplify 48/18 to 8/3, or 12:18:30 to 2:3:5.
Open LCM for a common multiple, or Factor to list one integer’s factors.

How it works

GCF, GCD and HCF are the same function: the largest positive integer that divides every input. 48 and 18 share 1, 2, 3 and 6; 6 is greatest. Euclid’s algorithm avoids listing: replace 48 by 48 mod 18 = 12, then 18 mod 12 = 6, then 12 mod 6 = 0, and 6 remains.

A list folds the same way: gcd(12, 18) = 6, gcd(6, 30) = 6. gcd(n, 0) is |n|. Signs are ignored.

Simplifying 48/18 is divide top and bottom by 6 → 8/3. A ratio 12:18:30 becomes 2:3:5. That is the usual reason to open this page instead of LCM.

Coprime pairs (8 and 15) have GCF 1. They still have an LCM (120). Do not expect GCF to “align calendars.”

This does not list every factor of one number — that is the factor calculator — and it does not compute LCM.

Three numbers can share a smaller GCF than any pair: gcd(8, 12) = 4 but gcd(8, 12, 18) = 2. Always fold the whole list. A leftover 1 means the set is coprime as a group even if some pairs are not.

Formula

gcd(a, b) = gcd(b, a mod b), until the remainder is 0
gcd(48, 18) = 6

Worked examples

Two numbers
48 and 18 → 6
Three numbers
12, 18, 30 → 6

Pairs people look up

Numbers	GCF
48, 18	6
12, 18, 30	6
8, 15	1
42, 56	14
12, 0	12
8, 12, 18	2

Useful notes

GCF = GCD = HCF.
gcd(n, 0) = |n|.
Use LCM for shared multiples, Factor for one integer’s list.

FAQ

How do I find the GCF of two numbers?: Use Euclid’s algorithm: replace the larger number by the remainder when it is divided by the smaller, and repeat until the remainder is 0. The last non-zero remainder is the GCF.
Is GCF the same as GCD?: Yes. Greatest common factor and greatest common divisor name the same integer.
What is gcd(12, 0)?: 12. Zero is a multiple of every integer, so the common factors of 12 and 0 are the factors of 12, and the greatest is 12.
How do I simplify 42/56 with this?: gcd(42, 56) = 14, so 42/56 = 3/4.
What is the GCF of 8 and 15?: 1. The numbers are coprime.

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