# Is 48 a prime number?

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

For 48, the answer is: No, 48 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 48) is as follows: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

For 48 to be a prime number, it would have been required that 48 has only two divisors, i.e., itself and 1.

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As a consequence:

- 48 is a multiple of 1
- 48 is a multiple of 2
- 48 is a multiple of 3
- 48 is a multiple of 4
- 48 is a multiple of 6
- 48 is a multiple of 8
- 48 is a multiple of 12
- 48 is a multiple of 16
- 48 is a multiple of 24

For 48 to be a prime number, it would have been required that 48 has only two divisors, i.e., itself and 1.

### Is 48 a deficient number?

No, 48 is not a deficient number: to be deficient, 48 should have been such that 48 is larger than the sum of its proper divisors, i.e., the divisors of 48 without 48 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 = 76).

In fact, 48 is an abundant number; 48 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 = 76). The smallest abundant number is 12.