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Is 13 a prime number?

13 is a prime number. Here is how to check it, one division at a time.

The answer

Yes. 13 is a prime number: its only factors are 1 and 13.

How to check that 13 is prime

Try dividing 13 by the prime numbers, starting with 2. You only need primes: if 4 went into 13, then 2 would too.

  1. 13 ÷ 2 = 6 remainder 1, so 2 is not a factor.
  2. 13 ÷ 3 = 4 remainder 1, so 3 is not a factor.

Stop at 5: 5 × 5 = 25, which is more than 13. Any factor bigger than that would need a partner smaller than 5, and you have already tried those. So 13 is prime.

Where 13 comes among the primes

13 is the 6th prime number. The prime just before it is 11.

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 13

  • 13 is not in any times table from 2 to 12. The answers either side of it are 12 (2 × 6, 3 × 4, 4 × 3, 6 × 2 and 12 × 1) and 14 (2 × 7 and 7 × 2).
  • The nearest square number is 16 (4 × 4), 3 above it.
  • Primes 4 apart are called cousin primes, and 13 has one cousin: 17.

13 at a glance

In words
thirteen
In Roman numerals
XIII
Odd or even
Odd: it ends in 3
Its factors add up to
14, or 1 without 13 itself, which makes 13 a deficient number

Related pages

More numbers

Questions parents ask

Is 13 one of a pair of twin primes?

Yes. Twin primes are two primes 2 apart, and 13 pairs with 11.

What is the next prime number after 13?

17, which is 4 more than 13. Every number in between has a factor other than 1 and itself.

What is 13 × 13?

13 × 13 = 169. The square of a prime has exactly three factors: 1, 13 and 169.

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.