Factors Calculator: Find All Factors of a Number
Type a whole number to list every factor, see them in pairs, and get the count and the sum of factors.
- Nothing you type is stored
- Free
- No signup
Number of factors
12
- Sum of all factors
- 168
- Prime factors
- 2² × 3 × 5
Show working
- 60 = 2² × 3 × 5
- (2 + 1) × (1 + 1) × (1 + 1) = 12
- 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factor pairs
| Factor | Paired factor |
|---|---|
| 1 | 60 |
| 2 | 30 |
| 3 | 20 |
| 4 | 15 |
| 5 | 12 |
| 6 | 10 |
How to use
- Type a whole number.
- Read how many factors it has, their sum and its prime factors.
- See all the factors in the steps and the factor pairs in the table.
Good to know
A factor divides a number exactly: the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. Factors come in pairs that multiply to the number (1 × 60, 2 × 30, 3 × 20…), so you only need to search up to the square root.
The count of factors comes from the prime factorisation: if n = p^a × q^b × …, it has (a + 1)(b + 1)… factors. 60 = 2² × 3 × 5, so it has 3 × 2 × 2 = 12. A number with exactly two factors is prime; a perfect square has an odd number of factors.
A perfect number equals the sum of its factors other than itself: 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14. The calculator flags these. Factors help with simplifying fractions, HCF and LCM, and arranging things in equal rows.
Questions
What are the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18 and 36. That's 9 factors; odd because 36 is a perfect square.
What is the difference between factors and multiples?
Factors divide a number (factors of 12: 1, 2, 3, 4, 6, 12). Multiples are the number times 1, 2, 3… (12, 24, 36…).
How do I find the number of factors quickly?
Write the prime factorisation, add 1 to each exponent and multiply. 72 = 2³ × 3², so (3 + 1)(2 + 1) = 12 factors.
Is 1 a factor of every number?
Yes, and every number is a factor of itself.
What is the smallest number with 10 factors?
48 = 2⁴ × 3, with (4 + 1)(1 + 1) = 10 factors.