CalcArcade.

Factor Calculator

Enter a whole number. You get all its factors, the factor pairs, the prime factorization and a few facts about the number.

Your numbers

Result

How we calculate it

A factor of n is a whole number that divides n exactly. The calculator tests every number from 1 up to the square root of n. Each one that divides n gives two factors, d and n ÷ d, which form a factor pair. The prime factorization is found by dividing out the primes in order.

For example, 12 has the factors 1, 2, 3, 4, 6 and 12, the pairs 1 × 12, 2 × 6 and 3 × 4, and the prime factorization 2^2 × 3. The factors add up to 28. A number is perfect when its factors other than itself add up to the number, abundant when they add up to more and deficient when they add up to less.

Assumptions and limits

  • The number must be a whole number from 1 to 1,000,000,000,000. A number with more than 200 factors shows the first 200, and the table shows the first 100 pairs.
  • A prime number has exactly two factors, 1 and itself. The number 1 is neither prime nor composite.
  • The first perfect numbers are 6, 28, 496 and 8128.

Frequently asked questions

What are the factors of 12?

The factors of 12 are 1, 2, 3, 4, 6 and 12. They make the pairs 1 × 12, 2 × 6 and 3 × 4.

What is the difference between a factor and a multiple?

A factor divides the number exactly, so 3 is a factor of 12. A multiple is what you get by multiplying the number, so 24 is a multiple of 12.

How do I know if a number is prime?

A prime has only two factors, 1 and itself. If the calculator lists more than two factors, the number is composite.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Number = 12.

  • Number of factors 6
  • Factors 1, 2, 3, 4, 6, 12
  • Sum of factors 28
  • Prime factorization 2^2 × 3
  • Prime or composite Composite
  • Perfect, abundant or deficient Abundant

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.