Factors of 91
The factors of 91 are 1, 7, 13, 91. No, 91 is a composite number. Its prime factorization is 7 × 13.
Factor pairs of 91
Every factor has a partner that multiplies with it to give 91. 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 91 | 1 × 91 = 91 |
| 7 and 13 | 7 × 13 = 91 |
Prime factorization of 91, 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 | 91 ÷ 7 | 13 |
| 2 | 13 ÷ 13 | 1 |
So 91 = 7 × 13, written compactly as 7 × 13.
Divisibility checks for 91
The quick rules a student uses before dividing, applied to 91:
| Divisible by | Rule | For 91 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 1 | no |
| 3 | digit sum divisible by 3 | digits add to 10 | no |
| 4 | last two digits divisible by 4 | 91 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 1 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 10 | no |
| 8 | last three digits divisible by 8 | 91 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 10 | no |
| 10 | last digit is 0 | last digit 1 | no |
Frequently Asked Questions
What are the factors of 91?
The factors of 91 are 1, 7, 13, 91.
Is 91 a prime number?
No, 91 is a composite number. Its prime factorization is 7 × 13.
How many factors does 91 have?
91 has 4 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 7 × 13 and multiply -- (1+1) × (1+1) = 4.
Is 91 even or odd?
91 is odd (2 is not a factor).
What is the sum of the factors of 91?
1 + 7 + 13 + 91 = 112. Leaving out 91 itself, the proper factors add to 21, less than 91, so 91 is a deficient number.
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