Is 204 a prime number? What are the divisors of 204?

## Is 204 a prime number?

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

For 204, the answer is: No, 204 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 204) is as follows: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204.

To be 204 a prime number, it would have been required that 204 has only two divisors, i.e., itself and 1.

As a consequence:

• 204 is a multiple of 1
• 204 is a multiple of 2
• 204 is a multiple of 3
• 204 is a multiple of 4
• 204 is a multiple of 6
• 204 is a multiple of 12
• 204 is a multiple of 17
• 204 is a multiple of 34
• 204 is a multiple of 51
• 204 is a multiple of 68
• 204 is a multiple of 102

To be 204 a prime number, it would have been required that 204 has only two divisors, i.e., itself and 1.

## Is 204 a deficient number?

No, 204 is not a deficient number: to be deficient, 204 should have been such that 204 is larger than the sum of its proper divisors, i.e., the divisors of 204 without 204 itself (that is 1 + 2 + 3 + 4 + 6 + 12 + 17 + 34 + 51 + 68 + 102 = 300).

In fact, 204 is an abundant number; 204 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 12 + 17 + 34 + 51 + 68 + 102 = 300). The smallest abundant number is 12.

## Parity of 204

204 is an even number, because it is evenly divisible by 2: 204 / 2 = 102.

## Is 204 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 204 is about 14.283.

Thus, the square root of 204 is not an integer, and therefore 204 is not a square number.

## What is the square number of 204?

The square of a number (here 204) is the result of the product of this number (204) by itself (i.e., 204 × 204); the square of 204 is sometimes called "raising 204 to the power 2", or "204 squared".

The square of 204 is 41 616 because 204 × 204 = 2042 = 41 616.

As a consequence, 204 is the square root of 41 616.

## Number of digits of 204

204 is a number with 3 digits.

## What are the multiples of 204?

The multiples of 204 are all integers evenly divisible by 204, that is all numbers such that the remainder of the division by 204 is zero. There are infinitely many multiples of 204. The smallest multiples of 204 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 204 too, since 0 × 204 = 0
• 204: indeed, 204 is a multiple of itself, since 204 is evenly divisible by 204 (we have 204 / 204 = 1, so the remainder of this division is indeed zero)
• 408: indeed, 408 = 204 × 2
• 612: indeed, 612 = 204 × 3
• 816: indeed, 816 = 204 × 4
• 1 020: indeed, 1 020 = 204 × 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 204). 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 14.283). 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 204

• Preceding numbers: …202, 203
• Following numbers: 205, 206

## Nearest numbers from 204

• Preceding prime number: 199
• Following prime number: 211
Find out whether some integer is a prime number