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Is 73 a prime number?

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

The answer

Yes. 73 is a prime number: its only factors are 1 and 73.

How to check that 73 is prime

Try dividing 73 by the prime numbers, starting with 2. You only need primes: if 4 went into 73, then 2 would too.

  1. 73 ÷ 2 = 36 remainder 1, so 2 is not a factor.
  2. 73 ÷ 3 = 24 remainder 1, so 3 is not a factor.
  3. 73 ÷ 5 = 14 remainder 3, so 5 is not a factor.
  4. 73 ÷ 7 = 10 remainder 3, so 7 is not a factor.

Stop at 11: 11 × 11 = 121, which is more than 73. Any factor bigger than that would need a partner smaller than 11, and you have already tried those. So 73 is prime.

Where 73 comes among the primes

73 is the 21st prime number. The prime just before it is 71.

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 73

  • 73 is not in any times table from 2 to 12. The answers either side of it are 72 (6 × 12, 8 × 9, 9 × 8 and 12 × 6) and 77 (7 × 11 and 11 × 7).
  • The nearest square number is 81 (9 × 9), 8 above it.

73 at a glance

In words
seventy-three
In Roman numerals
LXXIII
Odd or even
Odd: it ends in 3
Its factors add up to
74, or 1 without 73 itself, which makes 73 a deficient number

Related pages

More numbers

Questions parents ask

Is 73 one of a pair of twin primes?

Yes. Twin primes are two primes 2 apart, and 73 pairs with 71.

What is the next prime number after 73?

79, which is 6 more than 73. Every number in between has a factor other than 1 and itself.

What is 73 × 73?

73 × 73 = 5329. The square of a prime has exactly three factors: 1, 73 and 5329.

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.