Is 324 a prime number?

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

For 324, the answer is: No, 324 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 324) is as follows: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.

For 324 to be a prime number, it would have been required that 324 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

324 is a multiple of 1
324 is a multiple of 2
324 is a multiple of 3
324 is a multiple of 4
324 is a multiple of 6
324 is a multiple of 9
324 is a multiple of 12
324 is a multiple of 18
324 is a multiple of 27
324 is a multiple of 36
324 is a multiple of 54
324 is a multiple of 81
324 is a multiple of 108
324 is a multiple of 162

For 324 to be a prime number, it would have been required that 324 has only two divisors, i.e., itself and 1.

Is 324 a deficient number?

No, 324 is not a deficient number: to be deficient, 324 should have been such that 324 is larger than the sum of its proper divisors, i.e., the divisors of 324 without 324 itself (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 = 523).

In fact, 324 is an abundant number; 324 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 = 523). The smallest abundant number is 12.

Parity of 324

324 is an even number, because it is evenly divisible by 2: 324 / 2 = 162.

Find out more:

What is an even number?

Is 324 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 324 is 18.

Therefore, the square root of 324 is an integer, and as a consequence 324 is a perfect square.

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

What is the square number of 324?

The square of a number (here 324) is the result of the product of this number (324) by itself (i.e., 324 × 324); the square of 324 is sometimes called "raising 324 to the power 2", or "324 squared".

The square of 324 is 104 976 because 324 × 324 = 324² = 104 976.

As a consequence, 324 is the square root of 104 976.

Number of digits of 324

324 is a number with 3 digits.

What are the multiples of 324?

The multiples of 324 are all integers evenly divisible by 324, that is all numbers such that the remainder of the division by 324 is zero. There are infinitely many multiples of 324. The smallest multiples of 324 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 324 too, since 0 × 324 = 0
324: indeed, 324 is a multiple of itself, since 324 is evenly divisible by 324 (we have 324 / 324 = 1, so the remainder of this division is indeed zero)
648: indeed, 648 = 324 × 2
972: indeed, 972 = 324 × 3
1 296: indeed, 1 296 = 324 × 4
1 620: indeed, 1 620 = 324 × 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 324). 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 18). 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 324

Preceding numbers: …322, 323
Following numbers: 325, 326…

Nearest numbers from 324

Preceding prime number: 317
Following prime number: 331