CalcVind

HCF Calculator (GCF / GCD)

Greatest common factor of two or more numbers

Your Numbers

Separate numbers with commas or spaces.

Greatest Common Factor

12GCF of 48, 180
720
LCM
2² × 3
GCF as primes

Working

  1. 48 = 2⁴ × 3
  2. 180 = 2² × 3² × 5
  3. GCF = shared primes at their lowest power = 12
  5. Euclid's method:
  6. 180 = 3 × 48 + 36
  7. 48 = 1 × 36 + 12
  8. 36 = 3 × 12 + 0
  1. 1
    Enter the numbers
    Two or more whole numbers
  2. 2
    Press Find GCF
    Results update as you type
  3. 3
    See two methods
    Prime factors and Euclid

How is the GCF found?

The greatest common factor is the largest number that divides every input exactly. Two ways to find it:

Prime factors: multiply the primes they share, at the lowest power

Euclid: GCF(a, b) = GCF(b, a mod b), until the remainder is 0

Example

48 = 2⁴ × 3 and 180 = 2² × 3² × 5. They share 2² and 3, so the GCF is 4 × 3 = 12.

Where GCF is used

Simplifying fractions (divide top and bottom by the GCF), splitting things into equal groups, and cutting tiles or fabric into the largest equal squares.

Related calculators

Frequently asked questions

Is GCF the same as HCF?

Yes. Greatest common factor (GCF), highest common factor (HCF) and greatest common divisor (GCD) are three names for the same thing.

What does it mean if the GCF is 1?

The numbers are co-prime: they share no factor other than 1, like 8 and 15.

How do I use the GCF to simplify a fraction?

Divide the numerator and denominator by their GCF. 48/180 ÷ 12 = 4/15.

Last reviewed: October 2026