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.
- 73 ÷ 2 = 36 remainder 1, so 2 is not a factor.
- 73 ÷ 3 = 24 remainder 1, so 3 is not a factor.
- 73 ÷ 5 = 14 remainder 3, so 5 is not a factor.
- 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
Optional extra number facts:
- 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. 73 is deficient: Deficient means this sum is less than the 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.
Continue your number practice
Explore the diagnostic for another set of practice questions.