Is 72 a prime number?
72 is not a prime number. Here is the quickest way to see 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 the repeated primes written as powers, that is 2³ × 3².
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
- 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, which makes 72 an abundant 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.
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.