# Is 786 a prime number?

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

For 786, the answer is: No, 786 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 786) is as follows: 1, 2, 3, 6, 131, 262, 393, 786.

For 786 to be a prime number, it would have been required that 786 has only two divisors, i.e., itself and 1.

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As a consequence:

- 786 is a multiple of 1
- 786 is a multiple of 2
- 786 is a multiple of 3
- 786 is a multiple of 6
- 786 is a multiple of 131
- 786 is a multiple of 262
- 786 is a multiple of 393

For 786 to be a prime number, it would have been required that 786 has only two divisors, i.e., itself and 1.

### Is 786 a deficient number?

No, 786 is not a deficient number: to be deficient, 786 should have been such that 786 is larger than the sum of its proper divisors, i.e., the divisors of 786 without 786 itself (that is 1 + 2 + 3 + 6 + 131 + 262 + 393 = 798).

In fact, 786 is an abundant number; 786 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 131 + 262 + 393 = 798). The smallest abundant number is 12.