Is 422 a prime number?

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

For 422, the answer is: No, 422 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 422) is as follows: 1, 2, 211, 422.

For 422 to be a prime number, it would have been required that 422 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

422 is a multiple of 1
422 is a multiple of 2
422 is a multiple of 211

For 422 to be a prime number, it would have been required that 422 has only two divisors, i.e., itself and 1.

However, 422 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 422 = 2 x 211, where 2 and 211 are both prime numbers.

Is 422 a deficient number?

Yes, 422 is a deficient number, that is to say 422 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 422 without 422 itself (that is 1 + 2 + 211 = 214).

Parity of 422

422 is an even number, because it is evenly divisible by 2: 422 / 2 = 211.

Find out more:

What is an even number?

Is 422 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 422 is about 20.543.

Thus, the square root of 422 is not an integer, and therefore 422 is not a square number.

What is the square number of 422?

The square of a number (here 422) is the result of the product of this number (422) by itself (i.e., 422 × 422); the square of 422 is sometimes called "raising 422 to the power 2", or "422 squared".

The square of 422 is 178 084 because 422 × 422 = 422² = 178 084.

As a consequence, 422 is the square root of 178 084.

Number of digits of 422

422 is a number with 3 digits.

What are the multiples of 422?

The multiples of 422 are all integers evenly divisible by 422, that is all numbers such that the remainder of the division by 422 is zero. There are infinitely many multiples of 422. The smallest multiples of 422 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 422 too, since 0 × 422 = 0
422: indeed, 422 is a multiple of itself, since 422 is evenly divisible by 422 (we have 422 / 422 = 1, so the remainder of this division is indeed zero)
844: indeed, 844 = 422 × 2
1 266: indeed, 1 266 = 422 × 3
1 688: indeed, 1 688 = 422 × 4
2 110: indeed, 2 110 = 422 × 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 422). 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 20.543). 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 422

Preceding numbers: …420, 421
Following numbers: 423, 424…

Nearest numbers from 422

Preceding prime number: 421
Following prime number: 431