## Is 320 a prime number?

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

For 320, the answer is: No, 320 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 320) is as follows: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320.

To be 320 a prime number, it would have been required that 320 has only two divisors, i.e., itself and 1.

As a consequence:

- 320 is a multiple of 1
- 320 is a multiple of 2
- 320 is a multiple of 4
- 320 is a multiple of 5
- 320 is a multiple of 8
- 320 is a multiple of 10
- 320 is a multiple of 16
- 320 is a multiple of 20
- 320 is a multiple of 32
- 320 is a multiple of 40
- 320 is a multiple of 64
- 320 is a multiple of 80
- 320 is a multiple of 160

To be 320 a prime number, it would have been required that 320 has only two divisors, i.e., itself and 1.

## Is 320 a deficient number?

No, 320 is not a deficient number: to be deficient, 320 should have been such that 320 is larger than the sum of its proper divisors, i.e., the divisors of 320 without 320 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 32 + 40 + 64 + 80 + 160 = 442).

In fact, 320 is an abundant number; 320 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 32 + 40 + 64 + 80 + 160 = 442). The smallest abundant number is 12.

## Parity of 320

320 is an even number, because it is evenly divisible by 2: 320 / 2 = 160.

## Is 320 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 320 is about 17.889.

Thus, the square root of 320 is not an integer, and therefore 320 is not a square number.

## What is the square number of 320?

The square of a number (here 320) is the result of the product of this number (320) by itself (i.e., 320 × 320); the square of 320 is sometimes called "raising 320 to the power 2", or "320 squared".

The square of 320 is 102 400 because 320 × 320 = 320^{2} = 102 400.

As a consequence, 320 is the square root of 102 400.

## Number of digits of 320

320 is a number with 3 digits.

## What are the multiples of 320?

The multiples of 320 are all integers evenly divisible by 320, that is all numbers such that the remainder of the division by 320 is zero. There are infinitely many multiples of 320. The smallest multiples of 320 are:

- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 320 too, since 0 × 320 = 0
- 320: indeed, 320 is a multiple of itself, since 320 is evenly divisible by 320 (we have 320 / 320 = 1, so the remainder of this division is indeed zero)
- 640: indeed, 640 = 320 × 2
- 960: indeed, 960 = 320 × 3
- 1 280: indeed, 1 280 = 320 × 4
- 1 600: indeed, 1 600 = 320 × 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 320). 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 17.889). 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.