Enter two or more whole numbers to find the largest number that divides all of them, with the steps shown.
The greatest common factor, also called the greatest common divisor or highest common factor, is the largest whole number that divides every number in a set with no remainder. The GCF of 12 and 18 is 6, because 6 is the biggest number that goes into both. Finding the GCF is how you reduce a fraction to its lowest terms and how you split things into equal groups with nothing left over.
Write each number as a product of primes, then multiply the primes they all share, each taken to the lowest power that appears. For 12, 18 and 24, the factorizations are 2 × 2 × 3, 2 × 3 × 3 and 2 × 2 × 2 × 3. Every number has one 2 and one 3 in common, so the GCF is 2 × 3, which is 6. If the numbers share no prime factor, the GCF is 1, and the numbers are called coprime.
For big numbers, the Euclidean algorithm is much faster than factoring. Divide the larger number by the smaller, replace the larger with the remainder, and repeat until the remainder is 0. The last non-zero number is the GCF. This calculator uses it for numbers of any size, and shows the prime factorization steps when the numbers are up to about 10 trillion.
List the factors of each number and choose the biggest one they share, or multiply the shared prime factors from their prime factorizations.
It is 1, because two different primes share no factor other than 1.
It is 6. The factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 18 are 1, 2, 3, 6, 9, 18, and the biggest in common is 6.
Yes. Greatest common factor, greatest common divisor and highest common factor all name the same value.
Divide the top and bottom of a fraction by their GCF to reduce it to lowest terms. For 12/18 the GCF is 6, so the fraction is 2/3.
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