Pythagorist
Numbers

Factors Calculator

Find all the factors of any number. The calculator checks every possible divisor and presents all factor pairs, with full step-by-step working shown.

Factors of 48

12346812162448

10 factors

How it works

  1. Find all factor pairs

    Test each integer from 1 to √48 ≈ 6.93. For each divisor found, the quotient is also a factor.

  2. Factor pairs

    1×48,2×24,3×16,4×12,6×81 × 48, \quad 2 × 24, \quad 3 × 16, \quad 4 × 12, \quad 6 × 8

    Factor pairs of 48: 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8.

  3. All factors in order

    All factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

    Result:1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The formula

d is a factor of n  ⟺  nmod  d=0d \text{ is a factor of } n \iff n \mod d = 0
nnThe number
ddA potential factor

Example substitution

48÷6=8 (exact)⇒6 and 8 are both factors48 \div 6 = 8 \text{ (exact)} \Rightarrow 6 \text{ and } 8 \text{ are both factors}

Check each divisor up to √n. If it divides exactly, both d and n÷d are factors.

Worked examples

Find all factors of 24.

  1. 1
    1 × 24: ✓
  2. 2
    2 × 12: ✓
  3. 3
    3 × 8: ✓
  4. 4
    4 × 6: ✓
Answer: 1, 2, 3, 4, 6, 8, 12, 24

Find all factors of 36.

  1. 1
    1 × 36: ✓
  2. 2
    2 × 18: ✓
  3. 3
    3 × 12: ✓
  4. 4
    4 × 9: ✓
  5. 5
    6 × 6: ✓
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36

Find all factors of 100.

  1. 1
    1 × 100: ✓
  2. 2
    2 × 50: ✓
  3. 3
    4 × 25: ✓
  4. 4
    5 × 20: ✓
  5. 5
    10 × 10: ✓
Answer: 1, 2, 4, 5, 10, 20, 25, 50, 100

Frequently asked questions

What are factors?+

Factors of a number are whole numbers that divide into it exactly with no remainder. E.g., factors of 12 are 1, 2, 3, 4, 6, 12.

How do you find all factors of a number?+

Test each integer from 1 to the square root of the number. For each divisor found, the quotient is also a factor.

What are the factors of 36?+

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

What is the difference between factors and multiples?+

Factors divide into a number exactly. Multiples are the times-table results of a number.

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