# Is 966 a prime number?

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

For 966, the answer is: No, 966 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 966) is as follows: 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966.

For 966 to be a prime number, it would have been required that 966 has only two divisors, i.e., itself and 1.

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As a consequence:

- 966 is a multiple of 1
- 966 is a multiple of 2
- 966 is a multiple of 3
- 966 is a multiple of 6
- 966 is a multiple of 7
- 966 is a multiple of 14
- 966 is a multiple of 21
- 966 is a multiple of 23
- 966 is a multiple of 42
- 966 is a multiple of 46
- 966 is a multiple of 69
- 966 is a multiple of 138
- 966 is a multiple of 161
- 966 is a multiple of 322
- 966 is a multiple of 483

For 966 to be a prime number, it would have been required that 966 has only two divisors, i.e., itself and 1.

### Is 966 a deficient number?

No, 966 is not a deficient number: to be deficient, 966 should have been such that 966 is larger than the sum of its proper divisors, i.e., the divisors of 966 without 966 itself (that is 1 + 2 + 3 + 6 + 7 + 14 + 21 + 23 + 42 + 46 + 69 + 138 + 161 + 322 + 483 = 1 338).

In fact, 966 is an abundant number; 966 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 7 + 14 + 21 + 23 + 42 + 46 + 69 + 138 + 161 + 322 + 483 = 1 338). The smallest abundant number is 12.