## Is 300 a prime number?

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

For 300, the answer is: No, 300 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 300) is as follows: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300.

To be 300 a prime number, it would have been required that 300 has only two divisors, i.e., itself and 1.

As a consequence:

- 300 is a multiple of 1
- 300 is a multiple of 2
- 300 is a multiple of 3
- 300 is a multiple of 4
- 300 is a multiple of 5
- 300 is a multiple of 6
- 300 is a multiple of 10
- 300 is a multiple of 12
- 300 is a multiple of 15
- 300 is a multiple of 20
- 300 is a multiple of 25
- 300 is a multiple of 30
- 300 is a multiple of 50
- 300 is a multiple of 60
- 300 is a multiple of 75
- 300 is a multiple of 100
- 300 is a multiple of 150

To be 300 a prime number, it would have been required that 300 has only two divisors, i.e., itself and 1.

## Is 300 a deficient number?

No, 300 is not a deficient number: to be deficient, 300 should have been such that 300 is larger than the sum of its proper divisors, i.e., the divisors of 300 without 300 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 25 + 30 + 50 + 60 + 75 + 100 + 150 = 568).

In fact, 300 is an abundant number; 300 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 25 + 30 + 50 + 60 + 75 + 100 + 150 = 568). The smallest abundant number is 12.

## Parity of 300

300 is an even number, because it is evenly divisible by 2: 300 / 2 = 150.

## Is 300 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 300 is about 17.321.

Thus, the square root of 300 is not an integer, and therefore 300 is not a square number.

## What is the square number of 300?

The square of a number (here 300) is the result of the product of this number (300) by itself (i.e., 300 × 300); the square of 300 is sometimes called "raising 300 to the power 2", or "300 squared".

The square of 300 is 90 000 because 300 × 300 = 300^{2} = 90 000.

As a consequence, 300 is the square root of 90 000.

## Number of digits of 300

300 is a number with 3 digits.

## What are the multiples of 300?

The multiples of 300 are all integers evenly divisible by 300, that is all numbers such that the remainder of the division by 300 is zero. There are infinitely many multiples of 300. The smallest multiples of 300 are:

- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 300 too, since 0 × 300 = 0
- 300: indeed, 300 is a multiple of itself, since 300 is evenly divisible by 300 (we have 300 / 300 = 1, so the remainder of this division is indeed zero)
- 600: indeed, 600 = 300 × 2
- 900: indeed, 900 = 300 × 3
- 1 200: indeed, 1 200 = 300 × 4
- 1 500: indeed, 1 500 = 300 × 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 300). 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 17.321). 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.