## Is 40 a prime number?

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

For 40, the answer is: No, 40 is not a prime number.

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

To be 40 a prime number, it would have been required that 40 has only two divisors, i.e., itself and 1.

As a consequence:

- 40 is a multiple of 1
- 40 is a multiple of 2
- 40 is a multiple of 4
- 40 is a multiple of 5
- 40 is a multiple of 8
- 40 is a multiple of 10
- 40 is a multiple of 20

To be 40 a prime number, it would have been required that 40 has only two divisors, i.e., itself and 1.

## Is 40 a deficient number?

No, 40 is not a deficient number: to be deficient, 40 should have been such that 40 is larger than the sum of its proper divisors, i.e., the divisors of 40 without 40 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 = 50).

In fact, 40 is an abundant number; 40 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 = 50). The smallest abundant number is 12.

## Parity of 40

40 is an even number, because it is evenly divisible by 2: 40 / 2 = 20.

## Is 40 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 40 is about 6.325.

Thus, the square root of 40 is not an integer, and therefore 40 is not a square number.

## What is the square number of 40?

The square of a number (here 40) is the result of the product of this number (40) by itself (i.e., 40 × 40); the square of 40 is sometimes called "raising 40 to the power 2", or "40 squared".

The square of 40 is 1 600 because 40 × 40 = 40^{2} = 1 600.

As a consequence, 40 is the square root of 1 600.

## Number of digits of 40

40 is a number with 2 digits.

## What are the multiples of 40?

The multiples of 40 are all integers evenly divisible by 40, that is all numbers such that the remainder of the division by 40 is zero. There are infinitely many multiples of 40. The smallest multiples of 40 are:

- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 40 too, since 0 × 40 = 0
- 40: indeed, 40 is a multiple of itself, since 40 is evenly divisible by 40 (we have 40 / 40 = 1, so the remainder of this division is indeed zero)
- 80: indeed, 80 = 40 × 2
- 120: indeed, 120 = 40 × 3
- 160: indeed, 160 = 40 × 4
- 200: indeed, 200 = 40 × 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 40). 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 6.325). 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.