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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.

  1. 71 ÷ 2 = 35 remainder 1, so 2 is not a factor.
  2. 71 ÷ 3 = 23 remainder 2, so 3 is not a factor.
  3. 71 ÷ 5 = 14 remainder 1, so 5 is not a factor.
  4. 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.
  • Primes 4 apart are called cousin primes, and 71 has one cousin: 67.

71 at a glance

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, which makes 71 a deficient 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.

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.