Is 46 a prime number?

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

For 46, the answer is: No, 46 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 46) is as follows: 1, 2, 23, 46.

For 46 to be a prime number, it would have been required that 46 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

46 is a multiple of 1
46 is a multiple of 2
46 is a multiple of 23

For 46 to be a prime number, it would have been required that 46 has only two divisors, i.e., itself and 1.

However, 46 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 46 = 2 x 23, where 2 and 23 are both prime numbers.

Is 46 a deficient number?

Yes, 46 is a deficient number, that is to say 46 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 46 without 46 itself (that is 1 + 2 + 23 = 26).

Parity of 46

46 is an even number, because it is evenly divisible by 2: 46 / 2 = 23.

Find out more:

What is an even number?

Is 46 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 46 is about 6.782.

Thus, the square root of 46 is not an integer, and therefore 46 is not a square number.

What is the square number of 46?

The square of a number (here 46) is the result of the product of this number (46) by itself (i.e., 46 × 46); the square of 46 is sometimes called "raising 46 to the power 2", or "46 squared".

The square of 46 is 2 116 because 46 × 46 = 46² = 2 116.

As a consequence, 46 is the square root of 2 116.

Number of digits of 46

46 is a number with 2 digits.

What are the multiples of 46?

The multiples of 46 are all integers evenly divisible by 46, that is all numbers such that the remainder of the division by 46 is zero. There are infinitely many multiples of 46. The smallest multiples of 46 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 46 too, since 0 × 46 = 0
46: indeed, 46 is a multiple of itself, since 46 is evenly divisible by 46 (we have 46 / 46 = 1, so the remainder of this division is indeed zero)
92: indeed, 92 = 46 × 2
138: indeed, 138 = 46 × 3
184: indeed, 184 = 46 × 4
230: indeed, 230 = 46 × 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 46). 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 6.782). 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.

Numbers near 46

Preceding numbers: …44, 45
Following numbers: 47, 48…

Nearest numbers from 46

Preceding prime number: 43
Following prime number: 47