Factors of 31
The factors of 31 are 1, 31. Yes, 31 is a prime number. Its only factors are 1 and 31.
Factor pairs of 31
Every factor has a partner that multiplies with it to give 31. 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 31 | 1 × 31 = 31 |
Prime factorization of 31, step by step
31 is prime, so the ladder is one rung: nothing smaller than 31 divides it except 1. To confirm, you only need to test primes up to √31 ≈ 5: 31 ÷ 2 leaves 1; 31 ÷ 3 leaves 1; 31 ÷ 5 leaves 1.
Divisibility checks for 31
The quick rules a student uses before dividing, applied to 31:
| Divisible by | Rule | For 31 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 1 | no |
| 3 | digit sum divisible by 3 | digits add to 4 | no |
| 4 | last two digits divisible by 4 | 31 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 1 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 4 | no |
| 8 | last three digits divisible by 8 | 31 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 4 | no |
| 10 | last digit is 0 | last digit 1 | no |
Frequently Asked Questions
What are the factors of 31?
The factors of 31 are 1, 31.
Is 31 a prime number?
Yes, 31 is a prime number. Its only factors are 1 and 31.
How many factors does 31 have?
31 has 2 factors.
Is 31 even or odd?
31 is odd (2 is not a factor).
What is the sum of the factors of 31?
1 + 31 = 32. Leaving out 31 itself, the proper factors add to 1, less than 31, so 31 is a deficient number.
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