# Is 345 a prime number?

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

For 345, the answer is: No, 345 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 345) is as follows: 1, 3, 5, 15, 23, 69, 115, 345.

For 345 to be a prime number, it would have been required that 345 has only two divisors, i.e., itself and 1.

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Actually, one can immediately see that 345 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors.
The last digit of 345 is 5, so it is divisible by 5 and is therefore *not* prime.

As a consequence:

- 345 is a multiple of 1
- 345 is a multiple of 3
- 345 is a multiple of 5
- 345 is a multiple of 15
- 345 is a multiple of 23
- 345 is a multiple of 69
- 345 is a multiple of 115

For 345 to be a prime number, it would have been required that 345 has only two divisors, i.e., itself and 1.

### Is 345 a deficient number?

Yes, 345 is a deficient number, that is to say 345 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 345 without 345 itself (that is 1 + 3 + 5 + 15 + 23 + 69 + 115 = 231).