Is 67 a prime number?
67 is a prime number. Here is how to check it, one division at a time.
The answer
Yes. 67 is a prime number: its only factors are 1 and 67.
How to check that 67 is prime
Try dividing 67 by the prime numbers, starting with 2. You only need primes: if 4 went into 67, then 2 would too.
- 67 ÷ 2 = 33 remainder 1, so 2 is not a factor.
- 67 ÷ 3 = 22 remainder 1, so 3 is not a factor.
- 67 ÷ 5 = 13 remainder 2, so 5 is not a factor.
- 67 ÷ 7 = 9 remainder 4, so 7 is not a factor.
Stop at 11: 11 × 11 = 121, which is more than 67. Any factor bigger than that would need a partner smaller than 11, and you have already tried those. So 67 is prime.
Where 67 comes among the primes
67 is the 19th prime number. The prime just before it is 61.
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 67
- 67 is not in any times table from 2 to 12. The answers either side of it are 66 (6 × 11 and 11 × 6) and 70 (7 × 10 and 10 × 7).
- The nearest square number is 64 (8 × 8), 3 below it.
- Primes 4 apart are called cousin primes, and 67 has one cousin: 71.
67 at a glance
- In words
- sixty-seven
- In Roman numerals
- LXVII
- Odd or even
- Odd: it ends in 7
- Its factors add up to
- 68, or 1 without 67 itself, which makes 67 a deficient number
Related pages
More numbers
Questions parents ask
Is 67 one of a pair of twin primes?
No. Twin primes are two primes 2 apart, such as 11 and 13. Neither 65 nor 69 is prime, so 67 has no twin.
What is the next prime number after 67?
71, which is 4 more than 67. Every number in between has a factor other than 1 and itself.
What is 67 × 67?
67 × 67 = 4489. The square of a prime has exactly three factors: 1, 67 and 4489.
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.