## Is 225 a prime number?

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

For 225, the answer is: No, 225 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 225) is as follows: 1, 3, 5, 9, 15, 25, 45, 75, 225.

To be 225 a prime number, it would have been required that 225 has only two divisors, i.e., itself and 1.

As a consequence:

- 225 is a multiple of 1
- 225 is a multiple of 3
- 225 is a multiple of 5
- 225 is a multiple of 9
- 225 is a multiple of 15
- 225 is a multiple of 25
- 225 is a multiple of 45
- 225 is a multiple of 75

To be 225 a prime number, it would have been required that 225 has only two divisors, i.e., itself and 1.

## Is 225 a deficient number?

Yes, 225 is a deficient number, that is to say 225 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 225 without 225 itself (that is 1 + 3 + 5 + 9 + 15 + 25 + 45 + 75 = 178).

## Parity of 225

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

## Is 225 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 225 is 15.

Therefore, the square root of 225 is an integer, and as a consequence 225 is a perfect square.

As a consequence, 15 is the square root of 225.

## What is the square number of 225?

The square of a number (here 225) is the result of the product of this number (225) by itself (i.e., 225 × 225); the square of 225 is sometimes called "raising 225 to the power 2", or "225 squared".

The square of 225 is 50 625 because 225 × 225 = 225^{2} = 50 625.

As a consequence, 225 is the square root of 50 625.

## Number of digits of 225

225 is a number with 3 digits.

## What are the multiples of 225?

The multiples of 225 are all integers evenly divisible by 225, that is all numbers such that the remainder of the division by 225 is zero. There are infinitely many multiples of 225. The smallest multiples of 225 are:

- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 225 too, since 0 × 225 = 0
- 225: indeed, 225 is a multiple of itself, since 225 is evenly divisible by 225 (we have 225 / 225 = 1, so the remainder of this division is indeed zero)
- 450: indeed, 450 = 225 × 2
- 675: indeed, 675 = 225 × 3
- 900: indeed, 900 = 225 × 4
- 1 125: indeed, 1 125 = 225 × 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 225). 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 15). 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.