What is the greatest common factor?

The GCF (also called the HCF, highest common factor) is the largest whole number that divides every number in your list with no remainder. The GCF of 36 and 48 is 12.

How do you find the GCF with factor trees?

Split each number into pairs of factors until every branch ends in a prime. Multiply the primes that appear in every tree, using the smallest power each one appears with — that product is the GCF.

What does it mean when the GCF is 1?

It means the numbers share no prime factors at all — they are coprime. Consecutive numbers (like 14 and 15) are always coprime.

GCF vs LCM — which is which?

The GCF is the biggest number that fits inside all of your numbers; the LCM is the smallest number all of your numbers fit inside. We link the LCM calculator below if that is the one you need.

Arithmetic & Factors

Factor trees included

GCF Calculator

Enter two, three or four whole numbers and see the GCF emerge from factor trees and prime factorizations — not just an answer, but the whole argument for it.

Your numbers

Numbers to compare

2 numbers recognised

Two to four whole numbers between 1 and 100,000.

Worked solution

GCF of 36, 48

The largest whole number that divides all of them exactly

12 divides every one of 36, 48 with nothing left over, and no larger number does.

The working

4 steps

Break each number down to primes
Each branch splits a number into two factors, and keeps going until every branch ends in a prime (gold). Read the leaves bottom-up for the prime factorization.
Gold leaves are primes — multiply them together for the factorization.
Gold leaves are primes — multiply them together for the factorization.
Write each number as a product of primes
36
2² × 3²
48
2⁴ × 3
Keep only the primes every number shares
A prime counts toward the GCF only if it appears in every factorization — and only as many times as it appears in all of them (the smallest exponent wins).
Prime In 36 In 48 Shared?
2 2² 2⁴ 2²
3 3² 3 3
Multiply the shared primes together
GCF = 2² × 3 = 12
smallest exponent of each shared prime

Prime	In 36	In 48	Shared?
2	2²	2⁴	2²
3	3²	3	3

Works instantly in your browser — nothing is uploaded, and the URL keeps your numbers so you can share the exact worked example.

Why the smallest exponent wins

Take 36 = 2² × 3² and 48 = 2⁴ × 3. Any common factor can only use primes both numbers have, and it cannot use a prime more times than the number that has it fewest — otherwise it would not divide that number. So the GCF takes 2² (not 2⁴) and 3¹ (not 3²): 2² × 3 = 12.

Where the GCF is useful

Reducing fractions (divide top and bottom by the GCF), splitting things into equal groups, tiling a rectangle with the largest possible square tiles, and finding common denominators all lean on the GCF. It is also the engine inside the simplify calculator linked below.