# Is 728 a prime number?

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

For 728, the answer is: No, 728 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 728) is as follows: 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728.

For 728 to be a prime number, it would have been required that 728 has only two divisors, i.e., itself and 1.

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As a consequence:

- 728 is a multiple of 1
- 728 is a multiple of 2
- 728 is a multiple of 4
- 728 is a multiple of 7
- 728 is a multiple of 8
- 728 is a multiple of 13
- 728 is a multiple of 14
- 728 is a multiple of 26
- 728 is a multiple of 28
- 728 is a multiple of 52
- 728 is a multiple of 56
- 728 is a multiple of 91
- 728 is a multiple of 104
- 728 is a multiple of 182
- 728 is a multiple of 364

For 728 to be a prime number, it would have been required that 728 has only two divisors, i.e., itself and 1.

### Is 728 a deficient number?

No, 728 is not a deficient number: to be deficient, 728 should have been such that 728 is larger than the sum of its proper divisors, i.e., the divisors of 728 without 728 itself (that is 1 + 2 + 4 + 7 + 8 + 13 + 14 + 26 + 28 + 52 + 56 + 91 + 104 + 182 + 364 = 952).

In fact, 728 is an abundant number; 728 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 7 + 8 + 13 + 14 + 26 + 28 + 52 + 56 + 91 + 104 + 182 + 364 = 952). The smallest abundant number is 12.