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Factor Calculator

Find all factors and factor pairs of any positive integer.

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Factors of a Number — Complete Guide

A factor of a number is any integer that divides it exactly without a remainder. Every number greater than 1 has at least 2 factors: 1 and itself. Prime numbers have exactly 2 factors. Finding factors is essential for GCF/LCM, simplifying fractions, and understanding divisibility.

Number	All Factors	Number of Factors
12	1, 2, 3, 4, 6, 12	6
24	1, 2, 3, 4, 6, 8, 12, 24	8
36	1, 2, 3, 4, 6, 9, 12, 18, 36	9
100	1, 2, 4, 5, 10, 20, 25, 50, 100	9
Prime (e.g. 17)	1, 17	2

How to find all factors of a number?

To find factors: start from 1, divide the number by each integer up to its square root. If division is exact, both the divisor and quotient are factors. Example for 36: 36÷1=36, 36÷2=18, 36÷3=12, 36÷4=9, 36÷6=6 (stop at √36=6). Factors: 1,2,3,4,6,9,12,18,36.

What is a prime factor?

A prime factor is a factor that is also a prime number. Every integer greater than 1 can be expressed uniquely as a product of prime factors (Fundamental Theorem of Arithmetic). Example: 60 = 2² × 3 × 5 — the prime factors are 2, 3, and 5.