Factors of 9
The factors of 9 are 1, 3, 9. No, 9 is a composite number. Its prime factorization is 3^2.
Factor pairs of 9
Every factor has a partner that multiplies with it to give 9. 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 (here at 3 × 3), you have them all.
| Pair | Check |
|---|---|
| 1 and 9 | 1 × 9 = 9 |
| 3 and 3 | 3 × 3 = 9 |
Prime factorization of 9, 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 | 9 ÷ 3 | 3 |
| 2 | 3 ÷ 3 | 1 |
So 9 = 3 × 3, written compactly as 3^2.
Divisibility checks for 9
The quick rules a student uses before dividing, applied to 9:
| Divisible by | Rule | For 9 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 9 | no |
| 3 | digit sum divisible by 3 | digits add to 9 | yes |
| 4 | last two digits divisible by 4 | 9 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 9 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 9 | no |
| 8 | last three digits divisible by 8 | 9 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 9 | yes |
| 10 | last digit is 0 | last digit 9 | no |
Frequently Asked Questions
What are the factors of 9?
The factors of 9 are 1, 3, 9.
Is 9 a prime number?
No, 9 is a composite number. Its prime factorization is 3^2.
How many factors does 9 have?
9 has 3 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 3^2 and multiply -- (2+1) = 3.
Is 9 even or odd, and is it a perfect square?
9 is odd (2 is not a factor), and it is a perfect square: 3 × 3 = 9, which is why its factor list has an odd number of entries.
What is the sum of the factors of 9?
1 + 3 + 9 = 13. Leaving out 9 itself, the proper factors add to 4, less than 9, so 9 is a deficient number.
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