# Is 120 a prime number?

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

For 120, the answer is: No, 120 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 120) is as follows: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.

For 120 to be a prime number, it would have been required that 120 has only two divisors, i.e., itself and 1.

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Actually, one can immediately see that 120 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 120 is 0, so it is divisible by 5 and is therefore *not* prime.

As a consequence:

- 120 is a multiple of 1
- 120 is a multiple of 2
- 120 is a multiple of 3
- 120 is a multiple of 4
- 120 is a multiple of 5
- 120 is a multiple of 6
- 120 is a multiple of 8
- 120 is a multiple of 10
- 120 is a multiple of 12
- 120 is a multiple of 15
- 120 is a multiple of 20
- 120 is a multiple of 24
- 120 is a multiple of 30
- 120 is a multiple of 40
- 120 is a multiple of 60

For 120 to be a prime number, it would have been required that 120 has only two divisors, i.e., itself and 1.

### Is 120 a deficient number?

No, 120 is not a deficient number: to be deficient, 120 should have been such that 120 is larger than the sum of its proper divisors, i.e., the divisors of 120 without 120 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 = 240).

In fact, 120 is an abundant number; 120 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 = 240). The smallest abundant number is 12.