Is 72 a prime number?
72 is not a prime number. Here is a way to check it.
The answer
No. 72 is not a prime number: 2 × 36 = 72.
How to see that 72 is not prime
72 is even, and every even number can be divided by 2, so 2 is a factor as well as 1 and 72.
72 has 12 factors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72), which make 6 factor pairs.
Split 72 into prime factors
Split off the smallest prime each time, and keep going until every part is prime:
- 72 = 2 × 36
- 72 = 2 × 2 × 18
- 72 = 2 × 2 × 2 × 9
- 72 = 2 × 2 × 2 × 3 × 3
With repeated primes written as powers, that is 2³ × 3². A small raised number tells you how many times to use that factor: for example, 2³ means 2 × 2 × 2.
72 in the times tables
72 turns up in 4 different times tables, the 6, 8, 9 and 12: 6 × 12, 8 × 9, 9 × 8 and 12 × 6.
Quick checks that catch 72
- The last digit, 2, is even, so 2 goes in.
- The digits add up to 9, which is in the 3 times table, so 3 goes in.
- Half of it is 36, which is still even, so 4 goes in.
- It is even and passes the check for 3 as well, so 6 goes in.
- The digit total, 9, is a multiple of 9, so 9 goes in.
72 at a glance
Optional extra number facts:
- In words
- seventy-two
- In Roman numerals
- LXXII
- Odd or even
- Even: it ends in 2
- Its factors add up to
- 195, or 123 without 72 itself. 72 is abundant: Abundant means this sum is greater than the number.
The numbers either side of 72
- 71 is prime: 2, 3, 5 and 7 do not go into it, and 11 × 11 is already past 71. Check 71 in full
- 73 is prime: 2, 3, 5 and 7 do not go into it, and 11 × 11 is already past 73. Check 73 in full
Turn the digits round
72 backwards is 27. 27 is not prime. Its digits add up to 2 + 7 = 9, which is a multiple of 3. That means 27 is a multiple of 3 too, so 3 is a factor. Check 27 in full
Related pages
More numbers
Questions parents ask
Which prime numbers are either side of 72?
71 below it and 73 above it, a gap of 2.
What is 72 squared?
72 × 72 = 5184.
What is the smallest number with as many factors as 72?
60. It has 12 factors, the same as 72.
Continue your number practice
Explore the diagnostic for another set of practice questions.