How to find factors by hand
Test each whole number from 1 up to the square root of your number. Every time one divides evenly, you have found two factors: the divisor and the answer.
For 60, the square root is about 7.7, so you only test 1 to 7:
- 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10 (7 does not divide 60)
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Divisibility shortcuts
| Divisible by | Rule |
|---|
| 2 | Last digit is even |
| 3 | Digits add up to a multiple of 3 |
| 4 | Last two digits form a multiple of 4 |
| 5 | Ends in 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 9 | Digits add up to a multiple of 9 |
| 10 | Ends in 0 |
Special kinds of numbers
- Prime: exactly two factors (2, 3, 5, 7, 11…).
- Composite: more than two factors.
- Perfect square: an odd number of factors, because one pair repeats (36 = 6 × 6).
- Perfect number: the factors other than itself add up to the number, like 6 = 1 + 2 + 3 and 28.
Comparing the factors of several numbers? Use the GCF calculator or the LCM calculator.
Last reviewed October 2026.
Frequently asked questions
What are the factors of a number?
Factors are whole numbers that divide a number exactly, with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12, because each of them divides 12 evenly.
What is the difference between factors and prime factors?
Factors are every number that divides evenly. Prime factors are only the prime numbers that multiply together to make the number. For 12, the factors are 1, 2, 3, 4, 6, 12, while the prime factorization is 2 × 2 × 3.
How do I know if a number is prime?
A prime number has exactly two factors: 1 and itself. If the calculator lists only those two factors, the number is prime. The number 1 is not prime because it has only one factor.
What are factor pairs?
Factor pairs are two numbers that multiply to give the original number. For 24, the pairs are 1 × 24, 2 × 12, 3 × 8 and 4 × 6. They are useful for finding the dimensions of a rectangle with a given area.
Do negative numbers have factors?
Every positive factor also has a negative partner, since −2 × −6 = 12. By convention, factor lists in school usually show only the positive factors, which is what this calculator does.