Factor Calculator

Find all positive factors and factor pairs of a whole number

Your result will appear here.

About the Factor Calculator

Factors are whole numbers that divide another integer without leaving a remainder. Listing every factor is useful for divisibility problems, simplifying ratios and checking whether a number is prime or composite.

Factors come in pairs: if a×b equals the target number, then both a and b are factors.

How to Use the Factor Calculator

  1. Enter the integer you want to factor.
  2. Calculate the complete factor list.
  3. Review factor pairs if you want to understand how the divisors multiply back to the original number.
  4. Use prime factorization separately when you need only the prime building blocks.

How the Calculation Works

The calculator tests divisors up to the square root of the number. Whenever d divides n evenly, both d and n/d are factors.

Testing only to √n is sufficient because any factor larger than √n must be paired with a smaller factor already found.

Worked example

Factor Calculator Worked Example

Factors of 36

Factor pairs are 1×36, 2×18, 3×12, 4×9 and 6×6. The positive factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Result guide

Understanding Your Factor Calculator Result

The complete factor list shows every whole-number way the target can be divided evenly. Factor pairs also reveal whether the number has only the trivial pair 1×n or several non-trivial divisors.

Before you rely on the answer

Assumptions and Limitations

  • Input is an integer.
  • Positive factors are listed unless the tool explicitly supports negative factors.
  • Zero is not handled like an ordinary positive integer factor problem.

Practical tip

Using This Result in Practice

Use factor pairs when checking your work manually. Every factor below the square root should have a corresponding factor above it. For a perfect square, the square root appears as the middle factor paired with itself, so it should be counted only once in the factor list.

Related calculations

Useful Calculations to Continue With

If you need only the prime factors, use the Prime Factorization Calculator.

If you want the largest factor shared by several integers, use the GCF Calculator.

Common questions

Factor Calculator FAQ

Is 1 a factor of every positive integer?

Yes. Every positive integer is divisible by 1.

What is a factor pair?

It is a pair of integers whose product equals the target number.

How can factors tell me whether a number is prime?

A prime number has no positive factors other than 1 and itself.