# Is 114 a prime number?

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

For 114, the answer is: No, 114 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 114) is as follows: 1, 2, 3, 6, 19, 38, 57, 114.

For 114 to be a prime number, it would have been required that 114 has only two divisors, i.e., itself and 1.

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As a consequence:

- 114 is a multiple of 1
- 114 is a multiple of 2
- 114 is a multiple of 3
- 114 is a multiple of 6
- 114 is a multiple of 19
- 114 is a multiple of 38
- 114 is a multiple of 57

For 114 to be a prime number, it would have been required that 114 has only two divisors, i.e., itself and 1.

### Is 114 a deficient number?

No, 114 is not a deficient number: to be deficient, 114 should have been such that 114 is larger than the sum of its proper divisors, i.e., the divisors of 114 without 114 itself (that is 1 + 2 + 3 + 6 + 19 + 38 + 57 = 126).

In fact, 114 is an abundant number; 114 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 19 + 38 + 57 = 126). The smallest abundant number is 12.