# Is 60 a prime number?

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

For 60, the answer is: No, 60 is not a prime number.

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

For 60 to be a prime number, it would have been required that 60 has only two divisors, i.e., itself and 1.

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Actually, one can immediately see that 60 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 60 is 0, so it is divisible by 5 and is therefore *not* prime.

As a consequence:

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

For 60 to be a prime number, it would have been required that 60 has only two divisors, i.e., itself and 1.

### Is 60 a deficient number?

No, 60 is not a deficient number: to be deficient, 60 should have been such that 60 is larger than the sum of its proper divisors, i.e., the divisors of 60 without 60 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 = 108).

In fact, 60 is an abundant number; 60 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 = 108). The smallest abundant number is 12.