Is 91 a prime number?
91 is not a prime number. Here is the quickest way to see it.
The answer
No. 91 is not a prime number: 7 × 13 = 91.
How to see that 91 is not prime
91 is odd, its digits do not add up to a multiple of 3, and it does not end in 5, so the quick checks for 2, 3 and 5 all fail. Try 7 next: 7 × 13 = 91.
Up to 100, the only composite numbers that pass the checks for 2, 3 and 5 are 49, 77 and 91, and 7 goes into all three.
91 has four factors: 1 and 91, plus one pair in between, 7 and 13.
Why 91 looks prime
91 = 7 × 13, and 13 is beyond the 12 times table, so 7 × 13 is not a fact most children know by heart. That makes 91 easy to mistake for a prime.
Compare 89, the prime just below it. Try the same checks: 89 ÷ 2 = 44 remainder 1, 89 ÷ 3 = 29 remainder 2, 89 ÷ 5 = 17 remainder 4 and 89 ÷ 7 = 12 remainder 5. None goes in exactly, and 11 × 11 = 121 is more than 89, so 89 really is prime.
Split 91 into prime factors
91 splits straight into two primes, 7 × 13, so its factor tree has only one branch.
91 in the times tables
No fact from the 2 to 12 times tables, up to × 12, makes 91. Its smallest pair, 7 × 13, needs the 13 times table, which goes past 12.
See the 13 times table, where 13 × 7 = 91 is one of the facts.
Quick checks that catch 91
None of the digit checks work on 91: it is odd, its digit total is not a multiple of 3, and it does not end in 5 or 0. Only dividing by 7 finds a factor.
91 at a glance
- In words
- ninety-one
- In Roman numerals
- XCI
- Odd or even
- Odd: it ends in 1
- Triangular number
- 1 + 2 + … + 13 = 91, a triangle of counters with 13 on the bottom row
- Its factors add up to
- 112, or 21 without 91 itself, which makes 91 a deficient number
The numbers either side of 91
- 90 is not prime. 90 is even, and every even number can be divided by 2, so 2 is a factor as well as 1 and 90. Check 90 in full
- 92 is not prime. 92 is even, and every even number can be divided by 2, so 2 is a factor as well as 1 and 92. Check 92 in full
Turn the digits round
91 backwards is 19. 19 is prime: 2 and 3 do not go into it, and 5 × 5 is already past 19. Check 19 in full
Related pages
More numbers
Questions parents ask
Which prime numbers are either side of 91?
89 below it and 97 above it, a gap of 8.
What is 91 squared?
91 × 91 = 8281.
What is the smallest number with as many factors as 91?
6. It has 4 factors, the same as 91.
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.