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
- 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, which makes 31 a deficient 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.
Number facts are the base of 11+ maths
Factors, multiples, primes and square numbers come up all over 11+ maths, from simplifying fractions to ratio. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.