Is 71 a prime number?
71 is a prime number. Here is how to check it, one division at a time.
The answer
Yes. 71 is a prime number: its only factors are 1 and 71.
How to check that 71 is prime
Try dividing 71 by the prime numbers, starting with 2. You only need primes: if 4 went into 71, then 2 would too.
- 71 ÷ 2 = 35 remainder 1, so 2 is not a factor.
- 71 ÷ 3 = 23 remainder 2, so 3 is not a factor.
- 71 ÷ 5 = 14 remainder 1, so 5 is not a factor.
- 71 ÷ 7 = 10 remainder 1, so 7 is not a factor.
Stop at 11: 11 × 11 = 121, which is more than 71. Any factor bigger than that would need a partner smaller than 11, and you have already tried those. So 71 is prime.
Where 71 comes among the primes
71 is the 20th prime number. The prime just before it is 67.
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 71
- 71 is not in any times table from 2 to 12. The answers either side of it are 70 (7 × 10 and 10 × 7) and 72 (6 × 12, 8 × 9, 9 × 8 and 12 × 6).
- The nearest square number is 64 (8 × 8), 7 below it.
- Two prime numbers with a difference of 4 are called cousin primes. 71 has one cousin prime: 67.
71 at a glance
Optional extra number facts:
- In words
- seventy-one
- In Roman numerals
- LXXI
- Odd or even
- Odd: it ends in 1
- Its factors add up to
- 72, or 1 without 71 itself. 71 is deficient: Deficient means this sum is less than the number.
Related pages
More numbers
Questions parents ask
Is 71 one of a pair of twin primes?
Yes. Twin primes are two primes 2 apart, and 71 pairs with 73.
What is the next prime number after 71?
73, which is 2 more than 71. Every number in between has a factor other than 1 and itself.
What is 71 × 71?
71 × 71 = 5041. The square of a prime has exactly three factors: 1, 71 and 5041.
Continue your number practice
Explore the diagnostic for another set of practice questions.