# Is 20 a prime number?

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

For 20, the answer is: No, 20 is not a prime number.

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

For 20 to be a prime number, it would have been required that 20 has only two divisors, i.e., itself and 1.

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Actually, one can immediately see that 20 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 20 is 0, so it is divisible by 5 and is therefore *not* prime.

As a consequence:

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

For 20 to be a prime number, it would have been required that 20 has only two divisors, i.e., itself and 1.

### Is 20 a deficient number?

No, 20 is not a deficient number: to be deficient, 20 should have been such that 20 is larger than the sum of its proper divisors, i.e., the divisors of 20 without 20 itself (that is 1 + 2 + 4 + 5 + 10 = 22).

In fact, 20 is an abundant number; 20 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 10 = 22). The smallest abundant number is 12.