# Is 306 a prime number?

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

For 306, the answer is: No, 306 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 306) is as follows: 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.

For 306 to be a prime number, it would have been required that 306 has only two divisors, i.e., itself and 1.

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As a consequence:

- 306 is a multiple of 1
- 306 is a multiple of 2
- 306 is a multiple of 3
- 306 is a multiple of 6
- 306 is a multiple of 9
- 306 is a multiple of 17
- 306 is a multiple of 18
- 306 is a multiple of 34
- 306 is a multiple of 51
- 306 is a multiple of 102
- 306 is a multiple of 153

For 306 to be a prime number, it would have been required that 306 has only two divisors, i.e., itself and 1.

### Is 306 a deficient number?

No, 306 is not a deficient number: to be deficient, 306 should have been such that 306 is larger than the sum of its proper divisors, i.e., the divisors of 306 without 306 itself (that is 1 + 2 + 3 + 6 + 9 + 17 + 18 + 34 + 51 + 102 + 153 = 396).

In fact, 306 is an abundant number; 306 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 17 + 18 + 34 + 51 + 102 + 153 = 396). The smallest abundant number is 12.