Is 18 a prime number?

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

For 18, the answer is: No, 18 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 18) is as follows: 1, 2, 3, 6, 9, 18.

For 18 to be a prime number, it would have been required that 18 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

18 is a multiple of 1
18 is a multiple of 2
18 is a multiple of 3
18 is a multiple of 6
18 is a multiple of 9

For 18 to be a prime number, it would have been required that 18 has only two divisors, i.e., itself and 1.

Is 18 a deficient number?

No, 18 is not a deficient number: to be deficient, 18 should have been such that 18 is larger than the sum of its proper divisors, i.e., the divisors of 18 without 18 itself (that is 1 + 2 + 3 + 6 + 9 = 21).

In fact, 18 is an abundant number; 18 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 = 21). The smallest abundant number is 12.

Parity of 18

18 is an even number, because it is evenly divisible by 2: 18 / 2 = 9.

Find out more:

What is an even number?

Is 18 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 18 is about 4.243.

Thus, the square root of 18 is not an integer, and therefore 18 is not a square number.

What is the square number of 18?

The square of a number (here 18) is the result of the product of this number (18) by itself (i.e., 18 × 18); the square of 18 is sometimes called "raising 18 to the power 2", or "18 squared".

The square of 18 is 324 because 18 × 18 = 18² = 324.

As a consequence, 18 is the square root of 324.

Number of digits of 18

18 is a number with 2 digits.

What are the multiples of 18?

The multiples of 18 are all integers evenly divisible by 18, that is all numbers such that the remainder of the division by 18 is zero. There are infinitely many multiples of 18. The smallest multiples of 18 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 18 too, since 0 × 18 = 0
18: indeed, 18 is a multiple of itself, since 18 is evenly divisible by 18 (we have 18 / 18 = 1, so the remainder of this division is indeed zero)
36: indeed, 36 = 18 × 2
54: indeed, 54 = 18 × 3
72: indeed, 72 = 18 × 4
90: indeed, 90 = 18 × 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 18). 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 4.243). 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 18

Preceding numbers: …16, 17
Following numbers: 19, 20…

Nearest numbers from 18

Preceding prime number: 17
Following prime number: 19