Factors of 58
The factors of 58 are 1, 2, 29, 58. No, 58 is a composite number. Its prime factorization is 2 × 29.
Factor pairs of 58
Every factor has a partner that multiplies with it to give 58. 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 58 | 1 × 58 = 58 |
| 2 and 29 | 2 × 29 = 58 |
Prime factorization of 58, 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 | 58 ÷ 2 | 29 |
| 2 | 29 ÷ 29 | 1 |
So 58 = 2 × 29, written compactly as 2 × 29.
Divisibility checks for 58
The quick rules a student uses before dividing, applied to 58:
| Divisible by | Rule | For 58 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 8 | yes |
| 3 | digit sum divisible by 3 | digits add to 13 | no |
| 4 | last two digits divisible by 4 | 58 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 8 | no |
| 6 | divisible by both 2 and 3 | even, digit sum 13 | no |
| 8 | last three digits divisible by 8 | 58 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 13 | no |
| 10 | last digit is 0 | last digit 8 | no |
Frequently Asked Questions
What are the factors of 58?
The factors of 58 are 1, 2, 29, 58.
Is 58 a prime number?
No, 58 is a composite number. Its prime factorization is 2 × 29.
How many factors does 58 have?
58 has 4 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2 × 29 and multiply -- (1+1) × (1+1) = 4.
Is 58 even or odd?
58 is even (2 is one of its factors).
What is the sum of the factors of 58?
1 + 2 + 29 + 58 = 90. Leaving out 58 itself, the proper factors add to 32, less than 58, so 58 is a deficient number.
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