Factors Calculator: All Factors of a Number

This factors calculator lists every factor of a whole number — all the factors of 26 are 1, 2, 13 and 26 — together with the factor pairs, how many factors there are, and the prime factorization. It works for numbers up to one trillion.

Result

Enter values and press Calculate to see the result.

Formula

n=a×b  ⇒  a and b are factors of nn = a \times b \;\Rightarrow\; a \text{ and } b \text{ are factors of } n

Factors come in pairs; you only need to test divisors up to √n.

n=p1e1p2e2⋯  ⇒  #factors=(e1+1)(e2+1)⋯n = p_1^{e_1} p_2^{e_2} \cdots \;\Rightarrow\; \#\text{factors} = (e_1 + 1)(e_2 + 1)\cdots

The number of factors from the prime factorization.

How to use this calculator

  1. Type a positive whole number.
  2. Press Calculate to see all its factors, the factor pairs, the number of factors and the prime factorization.
  3. The steps test each number up to √n, so you can follow the method by hand.

Worked examples

All factors of 26

Test 1 to √26 ≈ 5.1: 1 × 26 and 2 × 13 work; 3, 4 and 5 don’t divide 26.

So the factors of 26 are 1, 2, 13 and 26.

Prime factorization: 26 = 2 × 13.

Factors of 54

Pairs up to √54 ≈ 7.3: 1 × 54, 2 × 27, 3 × 18, 6 × 9.

Factors: 1, 2, 3, 6, 9, 18, 27, 54.

54 = 2 × 3³, and (1 + 1)(3 + 1) = 8 factors ✓.

A square number: 36

Pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6 — the 6 is only counted once.

So 36 has 9 factors, an odd number, as every square does.

Common mistakes

  • Forgetting 1 and the number itself — they are always factors.
  • Stopping too early: test every whole number up to √n.
  • Counting a square root twice: 6 × 6 gives one factor, 6.
  • Confusing factors with multiples: factors of 26 divide it; multiples of 26 are 26, 52, 78…

Frequently asked questions

What are all the factors of 26?

1, 2, 13 and 26. The factor pairs are 1 × 26 and 2 × 13, and 26 = 2 × 13 in primes.

How do I find all the factors of a number?

Divide it by 1, 2, 3, … up to its square root. Every division with no remainder gives a factor pair; list both numbers in each pair.

What is the difference between factors and prime factors?

Factors are all the numbers that divide n exactly. Prime factors are only the primes among them, multiplied together to make n: the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, but its prime factorization is 2³ × 3.