Is 999 a prime number?

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

For 999, the answer is: No, 999 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 999) is as follows: 1, 3, 9, 27, 37, 111, 333, 999.

For 999 to be a prime number, it would have been required that 999 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

999 is a multiple of 1
999 is a multiple of 3
999 is a multiple of 9
999 is a multiple of 27
999 is a multiple of 37
999 is a multiple of 111
999 is a multiple of 333

For 999 to be a prime number, it would have been required that 999 has only two divisors, i.e., itself and 1.

Is 999 a deficient number?

Yes, 999 is a deficient number, that is to say 999 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 999 without 999 itself (that is 1 + 3 + 9 + 27 + 37 + 111 + 333 = 521).

Parity of 999

999 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 999 a perfect square number?

A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 999 is about 31.607.

Thus, the square root of 999 is not an integer, and therefore 999 is not a square number.

What is the square number of 999?

The square of a number (here 999) is the result of the product of this number (999) by itself (i.e., 999 × 999); the square of 999 is sometimes called "raising 999 to the power 2", or "999 squared".

The square of 999 is 998 001 because 999 × 999 = 999² = 998 001.

As a consequence, 999 is the square root of 998 001.

Number of digits of 999

999 is a number with 3 digits.

What are the multiples of 999?

The multiples of 999 are all integers evenly divisible by 999, that is all numbers such that the remainder of the division by 999 is zero. There are infinitely many multiples of 999. The smallest multiples of 999 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 999 too, since 0 × 999 = 0
999: indeed, 999 is a multiple of itself, since 999 is evenly divisible by 999 (we have 999 / 999 = 1, so the remainder of this division is indeed zero)
1 998: indeed, 1 998 = 999 × 2
2 997: indeed, 2 997 = 999 × 3
3 996: indeed, 3 996 = 999 × 4
4 995: indeed, 4 995 = 999 × 5
etc.

How to determine whether an integer is a prime number?

To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 999). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 31.607). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.

More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.

Numbers near 999

Preceding numbers: …997, 998
Following numbers: 1 000, 1 001…

Nearest numbers from 999

Preceding prime number: 997
Following prime number: 1 009