Find all factors, prime factors, and factor pairs of any number
A factor of a number is an integer that divides exactly into that number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Factors that are prime numbers (divisible only by 1 and themselves).
12 = 2 × 2 × 3
Two numbers that multiply together to make the original number.
12: (1,12), (2,6), (3,4)
Our Factor Calculator is a comprehensive online tool that helps you find all the factors of any positive integer. Whether you're a student learning number theory, a teacher preparing math lessons, or just curious about number properties, this calculator provides instant results with detailed information about your number.
Get all factors, prime factors, factor pairs, and prime factorization in one place.
See the prime factorization displayed as both an equation and a factor tree.
Learn about factors with our explanations and practical examples.
Number | Factors | Prime Factors | Factor Pairs |
---|---|---|---|
12 | 1, 2, 3, 4, 6, 12 | 2² × 3 | (1,12), (2,6), (3,4) |
17 | 1, 17 | 17 | (1,17) |
24 | 1, 2, 3, 4, 6, 8, 12, 24 | 2³ × 3 | (1,24), (2,12), (3,8), (4,6) |
Factors are all integers that divide evenly into a number. Prime factors are a subset of these - only the factors that are prime numbers. Every number can be expressed as a unique product of its prime factors.
Example for 36:
Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
Prime Factors: 2, 3 (since 36 = 2 × 2 × 3 × 3)
The most efficient method is to check divisibility up to the square root of the number:
Our calculator implements these methods to provide instant results.
Factors are fundamental in many areas of mathematics including: