Common Factor Calculator

A common factor is any whole number that divides evenly into every number in a group, not just one of them. Two numbers might each have plenty of factors on their own, but only the ones appearing in both lists actually count as common — and the largest of those shared factors is the greatest common factor (GCF), the number most people are really after.

It's the tool behind simplifying a fraction to lowest terms (dividing numerator and denominator by their GCF), splitting items into the largest possible equal groups, or figuring out the biggest square tile size that fits evenly across a rectangular floor with no cutting — all classic 'what's the biggest number that divides evenly into all of these' problems.

Common factors get harder to spot by inspection as more numbers are added to the list, which is exactly where working through the math systematically instead of guessing pays off.

This works by listing every factor of the first number, then narrowing that list down to only the factors that also divide evenly into every other number in the group — effectively an intersection of each number's individual factor set.

Whatever's left after that narrowing is the complete set of common factors, and the largest value remaining in that set is the greatest common factor (GCF) — the single number most simplification and grouping problems actually need.