# Is 138 a prime number?

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

For 138, the answer is: No, 138 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 138) is as follows: 1, 2, 3, 6, 23, 46, 69, 138.

For 138 to be a prime number, it would have been required that 138 has only two divisors, i.e., itself and 1.

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As a consequence:

- 138 is a multiple of 1
- 138 is a multiple of 2
- 138 is a multiple of 3
- 138 is a multiple of 6
- 138 is a multiple of 23
- 138 is a multiple of 46
- 138 is a multiple of 69

For 138 to be a prime number, it would have been required that 138 has only two divisors, i.e., itself and 1.

### Is 138 a deficient number?

No, 138 is not a deficient number: to be deficient, 138 should have been such that 138 is larger than the sum of its proper divisors, i.e., the divisors of 138 without 138 itself (that is 1 + 2 + 3 + 6 + 23 + 46 + 69 = 150).

In fact, 138 is an abundant number; 138 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 23 + 46 + 69 = 150). The smallest abundant number is 12.