Factor Calculator
Enter any whole number below to instantly find every factor, factor pair, and its prime factorization.
| Factor Pairs |
|---|
| 1 × 30 = 30 |
| 2 × 15 = 30 |
| 3 × 10 = 30 |
| 5 × 6 = 30 |
What Are Factors?
A factor of a number is a whole number that divides into it evenly, with nothing left over. Every number has at least two factors — 1 and itself — and most numbers have several more. Factors are the building blocks behind fraction simplification, GCF, LCM, and prime factorization.
How to Find All Factors of a Number, Step by Step
- Start with 1 and the number itself — these are always factors.
- Test each whole number from 2 up to the square root of the number. If it divides evenly, both it and the paired result are factors.
- Collect every factor found and sort them from smallest to largest.
Worked example
Find all factors of 36.
1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6 — the square root of 36 is exactly 6, so the search stops there.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Prime factorization: 36 = 2^2 × 3^2
Factors of Popular Numbers
Frequently Asked Questions
What is a factor of a number?
A factor of a number is a whole number that divides into it evenly, with no remainder. For example, 5 is a factor of 30 because 30 ÷ 5 = 6 exactly.
How do you find all the factors of a number?
Test each whole number from 1 up to the square root of the number. Whenever one divides evenly, both it and the paired result (the number divided by it) are factors. This is faster than checking every number up to the target itself, since factors always come in pairs.
What's the difference between a factor and a multiple?
A factor divides evenly into a number (factors of 12 include 1, 2, 3, 4, 6, 12). A multiple is what you get by multiplying a number by a whole number (multiples of 12 include 12, 24, 36, 48...). They're opposite directions of the same relationship.
What is prime factorization?
Prime factorization breaks a number down into the prime numbers that multiply together to make it — for example, 30 = 2 × 3 × 5. Every whole number greater than 1 has exactly one prime factorization (this is called the Fundamental Theorem of Arithmetic).
How many factors does a prime number have?
Exactly two: 1 and itself. That's the definition of a prime number. A composite number always has more than two factors.
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