# Is 272 a prime number?

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

For 272, the answer is: No, 272 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 272) is as follows: 1, 2, 4, 8, 16, 17, 34, 68, 136, 272.

For 272 to be a prime number, it would have been required that 272 has only two divisors, i.e., itself and 1.

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As a consequence:

- 272 is a multiple of 1
- 272 is a multiple of 2
- 272 is a multiple of 4
- 272 is a multiple of 8
- 272 is a multiple of 16
- 272 is a multiple of 17
- 272 is a multiple of 34
- 272 is a multiple of 68
- 272 is a multiple of 136

For 272 to be a prime number, it would have been required that 272 has only two divisors, i.e., itself and 1.

### Is 272 a deficient number?

No, 272 is not a deficient number: to be deficient, 272 should have been such that 272 is larger than the sum of its proper divisors, i.e., the divisors of 272 without 272 itself (that is 1 + 2 + 4 + 8 + 16 + 17 + 34 + 68 + 136 = 286).

In fact, 272 is an abundant number; 272 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 16 + 17 + 34 + 68 + 136 = 286). The smallest abundant number is 12.