# Is 522 a prime number?

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

For 522, the answer is: No, 522 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 522) is as follows: 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522.

For 522 to be a prime number, it would have been required that 522 has only two divisors, i.e., itself and 1.

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As a consequence:

- 522 is a multiple of 1
- 522 is a multiple of 2
- 522 is a multiple of 3
- 522 is a multiple of 6
- 522 is a multiple of 9
- 522 is a multiple of 18
- 522 is a multiple of 29
- 522 is a multiple of 58
- 522 is a multiple of 87
- 522 is a multiple of 174
- 522 is a multiple of 261

For 522 to be a prime number, it would have been required that 522 has only two divisors, i.e., itself and 1.

### Is 522 a deficient number?

No, 522 is not a deficient number: to be deficient, 522 should have been such that 522 is larger than the sum of its proper divisors, i.e., the divisors of 522 without 522 itself (that is 1 + 2 + 3 + 6 + 9 + 18 + 29 + 58 + 87 + 174 + 261 = 648).

In fact, 522 is an abundant number; 522 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 18 + 29 + 58 + 87 + 174 + 261 = 648). The smallest abundant number is 12.