Factors of 89
The factors of 89 are 1, 89. Yes, 89 is a prime number. Its only factors are 1 and 89.
Factor pairs of 89
Every factor has a partner that multiplies with it to give 89. 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 89 | 1 × 89 = 89 |
Prime factorization of 89, step by step
89 is prime, so the ladder is one rung: nothing smaller than 89 divides it except 1. To confirm, you only need to test primes up to √89 ≈ 9: 89 ÷ 2 leaves 1; 89 ÷ 3 leaves 2; 89 ÷ 5 leaves 4; 89 ÷ 7 leaves 5.
Divisibility checks for 89
The quick rules a student uses before dividing, applied to 89:
| Divisible by | Rule | For 89 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 9 | no |
| 3 | digit sum divisible by 3 | digits add to 17 | no |
| 4 | last two digits divisible by 4 | 89 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 9 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 17 | no |
| 8 | last three digits divisible by 8 | 89 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 17 | no |
| 10 | last digit is 0 | last digit 9 | no |
Frequently Asked Questions
What are the factors of 89?
The factors of 89 are 1, 89.
Is 89 a prime number?
Yes, 89 is a prime number. Its only factors are 1 and 89.
How many factors does 89 have?
89 has 2 factors.
Is 89 even or odd?
89 is odd (2 is not a factor).
What is the sum of the factors of 89?
1 + 89 = 90. Leaving out 89 itself, the proper factors add to 1, less than 89, so 89 is a deficient number.
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