Factor Calculator
Find the factors, factor pairs, and prime factorization of any whole number.
What are factors?
A factor of a number is a whole number that divides into it exactly, leaving no remainder. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, because each one divides evenly into 24. Every whole number greater than 1 has at least two factors: 1 and the number itself. Numbers with exactly two factors are called prime; numbers with more than two are composite.
How to find the factors of a number
- Start with 1 and the number itself — these are always factors.
- Test each whole number from 2 up to the square root of your number. If it divides evenly, both it and the result of the division are factors.
- Stop once you pass the square root — every factor beyond that point has already been found as a pair.
- List the factors in order from smallest to largest.
For example, to find the factors of 36 you only need to test up to 6 (since 6 × 6 = 36). Testing 1 through 6 gives the pairs 1×36, 2×18, 3×12, 4×9, and 6×6, for a full factor list of 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factor pairs
A factor pair is two factors that multiply together to make the original number. Listing factor pairs is a reliable way to check you've found every factor, since each one has a partner. For 24, the factor pairs are 1 × 24, 2 × 12, 3 × 8, and 4 × 6.
Prime factorization
Prime factorization writes a number as a product of prime numbers — numbers whose only factors are 1 and themselves. Every whole number greater than 1 has exactly one prime factorization (this is known as the fundamental theorem of arithmetic). For example, the prime factorization of 24 is 2³ × 3, since 24 = 2 × 2 × 2 × 3.
Factors of common numbers
Jump straight to the factors, factor pairs, and prime factorization of a specific number:
Related calculators
Need to factor an algebraic expression instead of a whole number? Try thefactoring calculator for quadratics, binomials, and cubics like x² + 5x + 6 or x³ - 8, with full step-by-step working.
Frequently asked questions
What is a factor?
A factor of a number is a whole number that divides into it exactly, with no remainder. For example, 4 is a factor of 12 because 12 ÷ 4 = 3 exactly. Every number has at least two factors: 1 and itself.
How do you find the factors of a number?
Divide the number by every whole number from 1 up to its square root. Whenever the division comes out exact, both the divisor and the result are factors. This calculator does that automatically and lists every factor in order.
What is a factor pair?
A factor pair is two numbers that multiply together to make the original number, such as 3 × 8 = 24. Every factor has a matching partner, so factor pairs are a quick way to check you have found every factor.
What is prime factorization?
Prime factorization breaks a number down into the prime numbers that multiply together to produce it, such as 24 = 2³ × 3. Every whole number greater than 1 has exactly one prime factorization.
How do I know if a number is prime?
A number is prime if it has exactly two factors: 1 and itself. If any other whole number divides it evenly, it is composite instead. This calculator checks that automatically for any number you enter.
Are negative numbers factors?
Every positive factor has a matching negative factor, since a negative times a negative also gives a positive result (for example, -4 × -6 = 24). This calculator focuses on positive factors, which is what "factors of a number" means in almost every school and everyday context.
Is this factor calculator free?
Yes. The factor calculator, factor pairs, and prime factorization results are free to use with no sign-up required.