# Is 1000 a prime number?

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

For 1000, the answer is: No, 1000 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 1000) is as follows: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.

For 1000 to be a prime number, it would have been required that 1000 has only two divisors, i.e., itself and 1.

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Actually, one can immediately see that 1 000 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 1 000 is 0, so it is divisible by 5 and is therefore *not* prime.

As a consequence:

- 1000 is a multiple of 1
- 1000 is a multiple of 2
- 1000 is a multiple of 4
- 1000 is a multiple of 5
- 1000 is a multiple of 8
- 1000 is a multiple of 10
- 1000 is a multiple of 20
- 1000 is a multiple of 25
- 1000 is a multiple of 40
- 1000 is a multiple of 50
- 1000 is a multiple of 100
- 1000 is a multiple of 125
- 1000 is a multiple of 200
- 1000 is a multiple of 250
- 1000 is a multiple of 500

For 1000 to be a prime number, it would have been required that 1000 has only two divisors, i.e., itself and 1.

### Is 1000 a deficient number?

No, 1000 is not a deficient number: to be deficient, 1000 should have been such that 1000 is larger than the sum of its proper divisors, i.e., the divisors of 1000 without 1000 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 + 125 + 200 + 250 + 500 = 1 340).

In fact, 1000 is an abundant number; 1000 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 + 125 + 200 + 250 + 500 = 1 340). The smallest abundant number is 12.