Factors of 59
The factors of 59 are 1, 59. Yes, 59 is a prime number. Its only factors are 1 and 59.
Factor pairs of 59
Every factor has a partner that multiplies with it to give 59. 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 59 | 1 × 59 = 59 |
Prime factorization of 59, step by step
59 is prime, so the ladder is one rung: nothing smaller than 59 divides it except 1. To confirm, you only need to test primes up to √59 ≈ 7: 59 ÷ 2 leaves 1; 59 ÷ 3 leaves 2; 59 ÷ 5 leaves 4; 59 ÷ 7 leaves 3.
Divisibility checks for 59
The quick rules a student uses before dividing, applied to 59:
| Divisible by | Rule | For 59 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 9 | no |
| 3 | digit sum divisible by 3 | digits add to 14 | no |
| 4 | last two digits divisible by 4 | 59 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 9 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 14 | no |
| 8 | last three digits divisible by 8 | 59 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 14 | no |
| 10 | last digit is 0 | last digit 9 | no |
Frequently Asked Questions
What are the factors of 59?
The factors of 59 are 1, 59.
Is 59 a prime number?
Yes, 59 is a prime number. Its only factors are 1 and 59.
How many factors does 59 have?
59 has 2 factors.
Is 59 even or odd?
59 is odd (2 is not a factor).
What is the sum of the factors of 59?
1 + 59 = 60. Leaving out 59 itself, the proper factors add to 1, less than 59, so 59 is a deficient number.
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