Factors of 60
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. No, 60 is a composite number. Its prime factorization is 2^2 × 3 × 5.
Factor pairs of 60
Every factor has a partner that multiplies with it to give 60. Listing pairs from the outside in is the fastest way to find all the factors: once the two numbers in a pair meet in the middle, you have them all.
| Pair | Check |
|---|---|
| 1 and 60 | 1 × 60 = 60 |
| 2 and 30 | 2 × 30 = 60 |
| 3 and 20 | 3 × 20 = 60 |
| 4 and 15 | 4 × 15 = 60 |
| 5 and 12 | 5 × 12 = 60 |
| 6 and 10 | 6 × 10 = 60 |
Prime factorization of 60, step by step
Divide by the smallest prime that goes in evenly, then repeat on the result until you reach 1. The divisors you used are the prime factors.
| Step | Divide | Result |
|---|---|---|
| 1 | 60 ÷ 2 | 30 |
| 2 | 30 ÷ 2 | 15 |
| 3 | 15 ÷ 3 | 5 |
| 4 | 5 ÷ 5 | 1 |
So 60 = 2 × 2 × 3 × 5, written compactly as 2^2 × 3 × 5.
Divisibility checks for 60
The quick rules a student uses before dividing, applied to 60:
| Divisible by | Rule | For 60 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 0 | yes |
| 3 | digit sum divisible by 3 | digits add to 6 | yes |
| 4 | last two digits divisible by 4 | 60 ÷ 4 | yes |
| 5 | last digit is 0 or 5 | last digit 0 | yes |
| 6 | divisible by both 2 and 3 | even, digit sum 6 | yes |
| 8 | last three digits divisible by 8 | 60 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 6 | no |
| 10 | last digit is 0 | last digit 0 | yes |
Frequently Asked Questions
What are the factors of 60?
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Is 60 a prime number?
No, 60 is a composite number. Its prime factorization is 2^2 × 3 × 5.
How many factors does 60 have?
60 has 12 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2^2 × 3 × 5 and multiply -- (2+1) × (1+1) × (1+1) = 12.
Is 60 even or odd?
60 is even (2 is one of its factors).
What is the sum of the factors of 60?
1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 + 60 = 168. Leaving out 60 itself, the proper factors add to 108, more than 60, so 60 is an abundant number.
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