Factor Calculator
List all the factors of a number, its factor pairs and its prime factorization.
Change the values and press Calculate to work out your own figures.
Enter a whole number to list every number that divides it exactly, in pairs, with its prime factorization.
| Pair |
|---|
| 1 × 120 |
| 2 × 60 |
| 3 × 40 |
| 4 × 30 |
| 5 × 24 |
| 6 × 20 |
| 8 × 15 |
| 10 × 12 |
Show the working
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
How to use it
Enter a whole number to list every number that divides it exactly, in pairs, with its prime factorization.
The answer is exact: whole numbers of any size up to 30 digits are handled without rounding, and Show the working lists every step.
Key facts
If n = p₁^a × p₂^b × …, it has (a + 1)(b + 1)… factors
Factors come in pairs
Every factor below the square root of a number pairs with one above it: for 120, 1 × 120, 2 × 60, 3 × 40 and so on. That is why you only need to test divisors up to the square root.
Questions
What are the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18 and 36.
How many factors does 120 have?
16, because 120 = 2³ × 3 × 5 and (3 + 1)(1 + 1)(1 + 1) = 16.
Formulas
If n = p₁^a × p₂^b × …, it has (a + 1)(b + 1)… factors
Sources
Limitations
- Numbers have at most 30 digits; factor lists and prime factorizations are limited to 10¹².