Factors of 120
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. No, 120 is a composite number. Its prime factorization is 2^3 × 3 × 5.
Factor pairs of 120
Every factor has a partner that multiplies with it to give 120. 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 120 | 1 × 120 = 120 |
| 2 and 60 | 2 × 60 = 120 |
| 3 and 40 | 3 × 40 = 120 |
| 4 and 30 | 4 × 30 = 120 |
| 5 and 24 | 5 × 24 = 120 |
| 6 and 20 | 6 × 20 = 120 |
| 8 and 15 | 8 × 15 = 120 |
| 10 and 12 | 10 × 12 = 120 |
Prime factorization of 120, 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 | 120 ÷ 2 | 60 |
| 2 | 60 ÷ 2 | 30 |
| 3 | 30 ÷ 2 | 15 |
| 4 | 15 ÷ 3 | 5 |
| 5 | 5 ÷ 5 | 1 |
So 120 = 2 × 2 × 2 × 3 × 5, written compactly as 2^3 × 3 × 5.
Divisibility checks for 120
The quick rules a student uses before dividing, applied to 120:
| Divisible by | Rule | For 120 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 0 | yes |
| 3 | digit sum divisible by 3 | digits add to 3 | yes |
| 4 | last two digits divisible by 4 | 20 ÷ 4 | yes |
| 5 | last digit is 0 or 5 | last digit 0 | yes |
| 6 | divisible by both 2 and 3 | even, digit sum 3 | yes |
| 8 | last three digits divisible by 8 | 120 ÷ 8 | yes |
| 9 | digit sum divisible by 9 | digits add to 3 | no |
| 10 | last digit is 0 | last digit 0 | yes |
Frequently Asked Questions
What are the factors of 120?
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Is 120 a prime number?
No, 120 is a composite number. Its prime factorization is 2^3 × 3 × 5.
How many factors does 120 have?
120 has 16 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2^3 × 3 × 5 and multiply -- (3+1) × (1+1) × (1+1) = 16.
Is 120 even or odd?
120 is even (2 is one of its factors).
What is the sum of the factors of 120?
1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 + 120 = 360. Leaving out 120 itself, the proper factors add to 240, more than 120, so 120 is an abundant number.
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