## Is 10 a prime number?

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

For 10, the answer is: No, 10 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 10) is as follows: 1, 2, 5, 10.

To be 10 a prime number, it would have been required that 10 has only two divisors, i.e., itself and 1.

As a consequence:

To be 10 a prime number, it would have been required that 10 has only two divisors, i.e., itself and 1.

However, 10 is a **semiprime** (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 10 = 2 x 5, where 2 and 5 are both prime numbers.

## Is 10 a deficient number?

Yes, 10 is a deficient number, that is to say 10 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 10 without 10 itself (that is 1 + 2 + 5 = 8).

## Parity of 10

10 is an even number, because it is evenly divisible by 2: 10 / 2 = 5.

## Is 10 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 10 is about 3.162.

Thus, the square root of 10 is not an integer, and therefore 10 is not a square number.

## What is the square number of 10?

The square of a number (here 10) is the result of the product of this number (10) by itself (i.e., 10 × 10); the square of 10 is sometimes called "raising 10 to the power 2", or "10 squared".

The square of 10 is 100 because 10 × 10 = 10^{2} = 100.

As a consequence, 10 is the square root of 100.

## Number of digits of 10

10 is a number with 2 digits.

## What are the multiples of 10?

The multiples of 10 are all integers evenly divisible by 10, that is all numbers such that the remainder of the division by 10 is zero. There are infinitely many multiples of 10. The smallest multiples of 10 are:

- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 10 too, since 0 × 10 = 0
- 10: indeed, 10 is a multiple of itself, since 10 is evenly divisible by 10 (we have 10 / 10 = 1, so the remainder of this division is indeed zero)
- 20: indeed, 20 = 10 × 2
- 30: indeed, 30 = 10 × 3
- 40: indeed, 40 = 10 × 4
- 50: indeed, 50 = 10 × 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 10). 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 3.162). 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.