# Is 9 a prime number?

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

For 9, the answer is: No, 9 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 9) is as follows: 1, 3, 9.

For 9 to be a prime number, it would have been required that 9 has only two divisors, i.e., itself and 1.

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As a consequence:

For 9 to be a prime number, it would have been required that 9 has only two divisors, i.e., itself and 1.

However, 9 is a **semiprime** (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 9 = 3 x 3, where 3 is a prime number.

### Is 9 a deficient number?

Yes, 9 is a deficient number, that is to say 9 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 9 without 9 itself (that is 1 + 3 = 4).