# Is 40 a prime number?

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

For 40, the answer is: No, 40 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 40) is as follows: 1, 2, 4, 5, 8, 10, 20, 40.

For 40 to be a prime number, it would have been required that 40 has only two divisors, i.e., itself and 1.

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Actually, one can immediately see that 40 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 40 is 0, so it is divisible by 5 and is therefore *not* prime.

As a consequence:

- 40 is a multiple of 1
- 40 is a multiple of 2
- 40 is a multiple of 4
- 40 is a multiple of 5
- 40 is a multiple of 8
- 40 is a multiple of 10
- 40 is a multiple of 20

For 40 to be a prime number, it would have been required that 40 has only two divisors, i.e., itself and 1.

### Is 40 a deficient number?

No, 40 is not a deficient number: to be deficient, 40 should have been such that 40 is larger than the sum of its proper divisors, i.e., the divisors of 40 without 40 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 = 50).

In fact, 40 is an abundant number; 40 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 = 50). The smallest abundant number is 12.