Is 990 a prime number?

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

For 990, the answer is: No, 990 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 990) is as follows: 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990.

For 990 to be a prime number, it would have been required that 990 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 990 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 990 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

990 is a multiple of 1
990 is a multiple of 2
990 is a multiple of 3
990 is a multiple of 5
990 is a multiple of 6
990 is a multiple of 9
990 is a multiple of 10
990 is a multiple of 11
990 is a multiple of 15
990 is a multiple of 18
990 is a multiple of 22
990 is a multiple of 30
990 is a multiple of 33
990 is a multiple of 45
990 is a multiple of 55
990 is a multiple of 66
990 is a multiple of 90
990 is a multiple of 99
990 is a multiple of 110
990 is a multiple of 165
990 is a multiple of 198
990 is a multiple of 330
990 is a multiple of 495

For 990 to be a prime number, it would have been required that 990 has only two divisors, i.e., itself and 1.

Is 990 a deficient number?

No, 990 is not a deficient number: to be deficient, 990 should have been such that 990 is larger than the sum of its proper divisors, i.e., the divisors of 990 without 990 itself (that is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 11 + 15 + 18 + 22 + 30 + 33 + 45 + 55 + 66 + 90 + 99 + 110 + 165 + 198 + 330 + 495 = 1 818).

In fact, 990 is an abundant number; 990 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 11 + 15 + 18 + 22 + 30 + 33 + 45 + 55 + 66 + 90 + 99 + 110 + 165 + 198 + 330 + 495 = 1 818). The smallest abundant number is 12.

Parity of 990

990 is an even number, because it is evenly divisible by 2: 990 / 2 = 495.

Find out more:

What is an even number?

Is 990 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 990 is about 31.464.

Thus, the square root of 990 is not an integer, and therefore 990 is not a square number.

What is the square number of 990?

The square of a number (here 990) is the result of the product of this number (990) by itself (i.e., 990 × 990); the square of 990 is sometimes called "raising 990 to the power 2", or "990 squared".

The square of 990 is 980 100 because 990 × 990 = 990² = 980 100.

As a consequence, 990 is the square root of 980 100.

Number of digits of 990

990 is a number with 3 digits.

What are the multiples of 990?

The multiples of 990 are all integers evenly divisible by 990, that is all numbers such that the remainder of the division by 990 is zero. There are infinitely many multiples of 990. The smallest multiples of 990 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 990 too, since 0 × 990 = 0
990: indeed, 990 is a multiple of itself, since 990 is evenly divisible by 990 (we have 990 / 990 = 1, so the remainder of this division is indeed zero)
1 980: indeed, 1 980 = 990 × 2
2 970: indeed, 2 970 = 990 × 3
3 960: indeed, 3 960 = 990 × 4
4 950: indeed, 4 950 = 990 × 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 990). 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 31.464). 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 990

Preceding numbers: …988, 989
Following numbers: 991, 992…

Nearest numbers from 990

Preceding prime number: 983
Following prime number: 991