# Is 702 a prime number?

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

For 702, the answer is: No, 702 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 702) is as follows: 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702.

For 702 to be a prime number, it would have been required that 702 has only two divisors, i.e., itself and 1.

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As a consequence:

- 702 is a multiple of 1
- 702 is a multiple of 2
- 702 is a multiple of 3
- 702 is a multiple of 6
- 702 is a multiple of 9
- 702 is a multiple of 13
- 702 is a multiple of 18
- 702 is a multiple of 26
- 702 is a multiple of 27
- 702 is a multiple of 39
- 702 is a multiple of 54
- 702 is a multiple of 78
- 702 is a multiple of 117
- 702 is a multiple of 234
- 702 is a multiple of 351

For 702 to be a prime number, it would have been required that 702 has only two divisors, i.e., itself and 1.

### Is 702 a deficient number?

No, 702 is not a deficient number: to be deficient, 702 should have been such that 702 is larger than the sum of its proper divisors, i.e., the divisors of 702 without 702 itself (that is 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 27 + 39 + 54 + 78 + 117 + 234 + 351 = 978).

In fact, 702 is an abundant number; 702 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 27 + 39 + 54 + 78 + 117 + 234 + 351 = 978). The smallest abundant number is 12.