Is 31 a prime number?
31 is a prime number. Here is how to check it, one division at a time.
The answer
Yes. 31 is a prime number: its only factors are 1 and 31.
How to check that 31 is prime
Try dividing 31 by the prime numbers, starting with 2. You only need primes: if 4 went into 31, then 2 would too.
- 31 ÷ 2 = 15 remainder 1, so 2 is not a factor.
- 31 ÷ 3 = 10 remainder 1, so 3 is not a factor.
- 31 ÷ 5 = 6 remainder 1, so 5 is not a factor.
Stop at 7: 7 × 7 = 49, which is more than 31. Any factor bigger than that would need a partner smaller than 7, and you have already tried those. So 31 is prime.
Where 31 comes among the primes
31 is the 11th prime number. The prime just before it is 29.
There are 25 prime numbers up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
Around 31
- 31 is not in any times table from 2 to 12. The answers either side of it are 30 (3 × 10, 5 × 6, 6 × 5 and 10 × 3) and 32 (4 × 8 and 8 × 4).
- The nearest square number is 36 (6 × 6), 5 above it.
31 at a glance
Optional extra number facts:
- In words
- thirty-one
- In Roman numerals
- XXXI
- Odd or even
- Odd: it ends in 1
- Its factors add up to
- 32, or 1 without 31 itself. 31 is deficient: Deficient means this sum is less than the number.
Related pages
More numbers
Questions parents ask
Is 31 one of a pair of twin primes?
Yes. Twin primes are two primes 2 apart, and 31 pairs with 29.
What is the next prime number after 31?
37, which is 6 more than 31. Every number in between has a factor other than 1 and itself.
What is 31 × 31?
31 × 31 = 961. The square of a prime has exactly three factors: 1, 31 and 961.
Continue your number practice
Explore the diagnostic for another set of practice questions.