# Is 805 a prime number?

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

For 805, the answer is: No, 805 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 805) is as follows: 1, 5, 7, 23, 35, 115, 161, 805.

For 805 to be a prime number, it would have been required that 805 has only two divisors, i.e., itself and 1.

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Actually, one can immediately see that 805 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 805 is 5, so it is divisible by 5 and is therefore *not* prime.

As a consequence:

- 805 is a multiple of 1
- 805 is a multiple of 5
- 805 is a multiple of 7
- 805 is a multiple of 23
- 805 is a multiple of 35
- 805 is a multiple of 115
- 805 is a multiple of 161

For 805 to be a prime number, it would have been required that 805 has only two divisors, i.e., itself and 1.

### Is 805 a deficient number?

Yes, 805 is a deficient number, that is to say 805 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 805 without 805 itself (that is 1 + 5 + 7 + 23 + 35 + 115 + 161 = 347).