Factor Calculator

The factors of a number are the whole numbers that divide it exactly. This factor calculator lists every factor in order, shows the factor pairs, and gives the prime factorisation. It also counts the factors, adds them up, and says whether the number is perfect, abundant or deficient.

Try:

How to use the factor calculator

  1. Enter a positive whole number, such as 36.
  2. Press Calculate.
  3. Read the factors, factor pairs and prime factorisation.

Formula

n=p1a1p2a2⋯⇒number of factors=(a1+1)(a2+1)⋯n = p_1^{a_1} p_2^{a_2} \cdots \Rightarrow \text{number of factors} = (a_1+1)(a_2+1)\cdots

Worked example: 36

  • Whole number: 36

✓ Answer checked

1, 2, 3, 4, 6, 9, 12, 18, 36

Factor pairs
1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
Number of factors
9
Prime factorisation
22×322^{2} \times 3^{2}
Sum of factors
91 (36 is abundant)
Step-by-step working (3 steps)

  1. Test divisors up to the square root

    Try each whole number from 1 up to √36 ≈ 6. Each divisor gives a pair.

  2. List the pairs

    Every factor below the square root pairs with one above it.

    1×36,  2×18,  3×12,  4×9,  6×61 \times 36,\; 2 \times 18,\; 3 \times 12,\; 4 \times 9,\; 6 \times 6

  3. Collect all factors

    Write every factor in order.

    9 factors9 \text{ factors}
Formulas used
If n=p1a1p2a2⋯ then the number of factors is (a1+1)(a2+1)⋯\text{If } n = p_1^{a_1} p_2^{a_2}\cdots \text{ then the number of factors is } (a_1+1)(a_2+1)\cdots
How this was checked
  • ✓ Every listed number divides exactly.
  • ✓ The prime-factor formula also gives 9 factors.

Frequently asked questions

What are the factors of 36?

1, 2, 3, 4, 6, 9, 12, 18 and 36.

What is a factor pair?

Two numbers that multiply to give the number. For 36, the pairs include 4 × 9 and 6 × 6.

What is a perfect number?

A number whose factors, other than itself, add up to the number. 28 is perfect: 1 + 2 + 4 + 7 + 14 = 28.

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