Factors of 99
The factors of 99 are 1, 3, 9, 11, 33, 99. No, 99 is a composite number. Its prime factorization is 3^2 × 11.
Factor pairs of 99
Every factor has a partner that multiplies with it to give 99. 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 99 | 1 × 99 = 99 |
| 3 and 33 | 3 × 33 = 99 |
| 9 and 11 | 9 × 11 = 99 |
Prime factorization of 99, 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 | 99 ÷ 3 | 33 |
| 2 | 33 ÷ 3 | 11 |
| 3 | 11 ÷ 11 | 1 |
So 99 = 3 × 3 × 11, written compactly as 3^2 × 11.
Divisibility checks for 99
The quick rules a student uses before dividing, applied to 99:
| Divisible by | Rule | For 99 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 9 | no |
| 3 | digit sum divisible by 3 | digits add to 18 | yes |
| 4 | last two digits divisible by 4 | 99 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 9 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 18 | no |
| 8 | last three digits divisible by 8 | 99 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 18 | yes |
| 10 | last digit is 0 | last digit 9 | no |
Frequently Asked Questions
What are the factors of 99?
The factors of 99 are 1, 3, 9, 11, 33, 99.
Is 99 a prime number?
No, 99 is a composite number. Its prime factorization is 3^2 × 11.
How many factors does 99 have?
99 has 6 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 3^2 × 11 and multiply -- (2+1) × (1+1) = 6.
Is 99 even or odd?
99 is odd (2 is not a factor).
What is the sum of the factors of 99?
1 + 3 + 9 + 11 + 33 + 99 = 156. Leaving out 99 itself, the proper factors add to 57, less than 99, so 99 is a deficient number.
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