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GCF Calculator

By Calxy · Updated · Calculation methodology

Find the biggest whole number that divides every number in your list exactly, then use it to make a ratio or fraction simpler.

Printed from Calxy · https://www.calxy.net/math/gcf-calculator

Type 2 to 100 whole numbers, separated by commas or spaces, such as 48, 180. Each can be up to 10¹². Minus signs are ignored. Decimals, 0 and other text are not allowed.

Greatest common factor

12

GCF(48, 180) = 12 · LCM = 720

  • 48 =2^4 × 3
  • 180 =2^2 × 3^2 × 5
  • Common factors1, 2, 3, 4, 6, 12
  • Greatest common factor12
  • Divided by 124 : 15

How this was calculated

  1. List every number that divides each of your numbers with nothing left over. These are its factors (numbers that divide it exactly).Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  2. Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
  3. Find the factors that appear in every list. The biggest one is the greatest common factor (GCF).Common factors: 1, 2, 3, 4, 6, 12Answer: GCF = 12
  4. Check it another way. Break each number into primes (numbers that only 1 and themselves divide). Keep the primes every number shares, using the smallest power of each, and multiply them.48 = 2^4 × 3; 180 = 2^2 × 3^2 × 5Put in your numbers: Shared primes: 2^2 × 3Answer: GCF = 12
  5. Euclid’s method is quickest for big numbers. Divide the bigger number by the smaller one and keep the remainder (what is left over). Then divide the smaller number by that remainder. Repeat until the remainder is 0. The last number you divided by is the GCF.180 = 3 × 48 + 36; 48 = 1 × 36 + 12; 36 = 3 × 12 + 0Answer: GCF(180, 48) = 12
  6. Divide each number by the GCF to get the smallest whole numbers in the same ratio.48 ÷ 12 = 4; 180 ÷ 12 = 15Answer: 4 : 15

The GCF in simple words

A factor is a number that divides another number exactly, with nothing left over. 3 is a factor of 12 because 12 ÷ 3 = 4.

The greatest common factor (GCF) is the biggest number that is a factor of all your numbers. It is also called the greatest common divisor (GCD) or highest common factor (HCF).

Example: the factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 18 are 1, 2, 3, 6, 9 and 18. The numbers in both lists are 1, 2, 3 and 6. The biggest is 6, so the GCF of 12 and 18 is 6.

The GCF helps you make fractions simpler. Divide the top and bottom of 12/18 by 6 and you get 2/3.

Euclid’s algorithm and shared prime factors

The greatest common factor (GCF), greatest common divisor (GCD), and highest common factor (HCF) name the same value. Euclid’s algorithm repeatedly replaces a pair with its divisor and remainder until the remainder is zero. The final non-zero divisor is the GCF.

For more than two inputs, find the GCF of the first pair and combine that result with each remaining input. In prime factorization, the same answer comes from keeping only shared primes, each at its lowest exponent.

Example: reducing 48 : 180

180 = 3 × 48 + 36; 48 = 1 × 36 + 12; 36 = 3 × 12 + 0. The GCF is 12. Dividing both terms by 12 reduces 48 : 180 to 4 : 15. The common positive factors are 1, 2, 3, 4, 6 and 12.

Input conventions

This page accepts 2–100 non-zero integers, each within ±10¹², and uses their absolute values. Negative signs do not change the positive GCF. Decimals and invalid tokens are rejected rather than omitted.

The optional LCM is reported only when it fits safe integer precision. That limit does not prevent a valid GCF from being shown.

Frequently asked questions

What does a GCF of 1 mean?

The entire list shares no positive divisor larger than 1. With three or more numbers this does not imply that every pair is coprime: 6, 10 and 15 have overall GCF 1, but each pair shares a factor.

Can I reduce a fraction using the GCF?

Yes. Divide numerator and denominator by their GCF. For 48/180, dividing both by 12 gives 4/15. A denominator must not be zero.

Last updated . Results are estimates for informational purposes only.