Factors of 90
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. No, 90 is a composite number. Its prime factorization is 2 × 3^2 × 5.
Factor pairs of 90
Every factor has a partner that multiplies with it to give 90. 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 90 | 1 × 90 = 90 |
| 2 and 45 | 2 × 45 = 90 |
| 3 and 30 | 3 × 30 = 90 |
| 5 and 18 | 5 × 18 = 90 |
| 6 and 15 | 6 × 15 = 90 |
| 9 and 10 | 9 × 10 = 90 |
Prime factorization of 90, 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 | 90 ÷ 2 | 45 |
| 2 | 45 ÷ 3 | 15 |
| 3 | 15 ÷ 3 | 5 |
| 4 | 5 ÷ 5 | 1 |
So 90 = 2 × 3 × 3 × 5, written compactly as 2 × 3^2 × 5.
Divisibility checks for 90
The quick rules a student uses before dividing, applied to 90:
| Divisible by | Rule | For 90 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 0 | yes |
| 3 | digit sum divisible by 3 | digits add to 9 | yes |
| 4 | last two digits divisible by 4 | 90 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 0 | yes |
| 6 | divisible by both 2 and 3 | even, digit sum 9 | yes |
| 8 | last three digits divisible by 8 | 90 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 9 | yes |
| 10 | last digit is 0 | last digit 0 | yes |
Frequently Asked Questions
What are the factors of 90?
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Is 90 a prime number?
No, 90 is a composite number. Its prime factorization is 2 × 3^2 × 5.
How many factors does 90 have?
90 has 12 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2 × 3^2 × 5 and multiply -- (1+1) × (2+1) × (1+1) = 12.
Is 90 even or odd?
90 is even (2 is one of its factors).
What is the sum of the factors of 90?
1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90 = 234. Leaving out 90 itself, the proper factors add to 144, more than 90, so 90 is an abundant number.
More Number Theory
- Factor Calculator (look up any number)
- GCF Calculator
- LCM Calculator
- LCD Calculator