Factor Pairs Explained: Find Every Divisor of a Number (2026)

A factor pair is two whole numbers that multiply to give your target number — and listing all of them reveals every divisor at once. Pairing factors up to the square root is the fastest way to find them all by hand.

This guide explains factor pairs, how to find every divisor without missing any, what the factor count tells you, and how to verify it in the Factors Calculator.

What is a factor pair?

A factor (or divisor) of a number divides it with no remainder. A factor pair is two factors that multiply to the number: for 12 the pairs are 1×12, 2×6 and 3×4. Every factor belongs to exactly one pair.

Find every divisor by pairing

Test each whole number from 1 upward. Whenever it divides evenly, you have found two factors: the divisor and its partner (number ÷ divisor). Stop once you reach the square root — beyond it the pairs simply repeat in reverse.

Worked example: factors of 36

Test up to √36 = 6: 1×36, 2×18, 3×12, 4×9, 6×6. That gives the factors 1, 2, 3, 4, 6, 9, 12, 18, 36 — nine in total. Because 36 is a perfect square, 6 pairs with itself, which is why the count is odd.

What the factor count means

An odd number of factors means the number is a perfect square. A number with exactly two factors is prime. You can read the factor count, the sum of factors and whether a number is prime straight from the Factors Calculator. To see the prime building blocks instead, use prime factorization.

Real-world uses

Factor pairs answer practical questions: the ways to arrange 36 chairs in equal rows, the possible rectangle dimensions with whole-number sides, or which group sizes split a class evenly. They are also the first step in simplifying fractions and finding the GCF.