# Is 415 a prime number?

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

For 415, the answer is: No, 415 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 415) is as follows: 1, 5, 83, 415.

For 415 to be a prime number, it would have been required that 415 has only two divisors, i.e., itself and 1.

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Actually, one can immediately see that 415 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 415 is 5, so it is divisible by 5 and is therefore *not* prime.

As a consequence:

For 415 to be a prime number, it would have been required that 415 has only two divisors, i.e., itself and 1.

However, 415 is a **semiprime** (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 415 = 5 x 83, where 5 and 83 are both prime numbers.

### Is 415 a deficient number?

Yes, 415 is a deficient number, that is to say 415 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 415 without 415 itself (that is 1 + 5 + 83 = 89).