Common Factor Calculator

This tool finds the factors that a group of numbers have in common. Rather than comparing long factor lists by eye, it computes the greatest common factor first and then lists that number's divisors, since every common factor must divide the greatest one.

What is a factor?

A factor of a whole number is a whole number that divides it exactly, with no remainder. The factors of 75 are 1, 3, 5, 15, 25 and 75, because each of these goes into 75 a whole number of times. Factors appear in pairs that multiply to the original number, such as 3 × 25 and 5 × 15, so you can find them all by testing divisors up to the square root and recording both members of each pair.

Every whole number has 1 and itself as factors. Numbers with no other factors are prime; the rest are composite.

What is a common factor?

A common factor of two or more numbers is a number that is a factor of each of them. Comparing the factors of 330 (1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330) with those of 75 (1, 3, 5, 15, 25, 75), the numbers on both lists are 1, 3, 5 and 15. Adding 450 and 225 to the comparison does not remove any of them, so those four are the common factors of the whole set.

The largest common factor, here 15, is the greatest common factor. Every other common factor divides it, so listing the factors of the GCF gives the complete set of common factors. The number 1 is a common factor of every set of whole numbers; if it is the only one, the numbers are called coprime.

Common factors help when dividing things into equal groups. With 330 red and 75 blue beads, you could make 3, 5 or 15 identical bracelets that use every bead, and 15 is the most possible. Common factors also make fraction simplification easy: dividing the top and bottom of 75/450 by the common factor 75 leaves 1/6.

Frequently asked questions