# Is 108 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 108, the answer is: No, 108 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 108) is as follows: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.

For 108 to be a prime number, it would have been required that 108 has only two divisors, i.e., itself and 1.

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As a consequence:

- 108 is a multiple of 1
- 108 is a multiple of 2
- 108 is a multiple of 3
- 108 is a multiple of 4
- 108 is a multiple of 6
- 108 is a multiple of 9
- 108 is a multiple of 12
- 108 is a multiple of 18
- 108 is a multiple of 27
- 108 is a multiple of 36
- 108 is a multiple of 54

For 108 to be a prime number, it would have been required that 108 has only two divisors, i.e., itself and 1.

### Is 108 a deficient number?

No, 108 is not a deficient number: to be deficient, 108 should have been such that 108 is larger than the sum of its proper divisors, i.e., the divisors of 108 without 108 itself (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 = 172).

In fact, 108 is an abundant number; 108 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 = 172). The smallest abundant number is 12.