Is 423 a prime number?

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

For 423, the answer is: No, 423 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 423) is as follows: 1, 3, 9, 47, 141, 423.

For 423 to be a prime number, it would have been required that 423 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

423 is a multiple of 1
423 is a multiple of 3
423 is a multiple of 9
423 is a multiple of 47
423 is a multiple of 141

For 423 to be a prime number, it would have been required that 423 has only two divisors, i.e., itself and 1.

Is 423 a deficient number?

Yes, 423 is a deficient number, that is to say 423 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 423 without 423 itself (that is 1 + 3 + 9 + 47 + 141 = 201).

Parity of 423

423 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 423 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 423 is about 20.567.

Thus, the square root of 423 is not an integer, and therefore 423 is not a square number.

What is the square number of 423?

The square of a number (here 423) is the result of the product of this number (423) by itself (i.e., 423 × 423); the square of 423 is sometimes called "raising 423 to the power 2", or "423 squared".

The square of 423 is 178 929 because 423 × 423 = 423² = 178 929.

As a consequence, 423 is the square root of 178 929.

Number of digits of 423

423 is a number with 3 digits.

What are the multiples of 423?

The multiples of 423 are all integers evenly divisible by 423, that is all numbers such that the remainder of the division by 423 is zero. There are infinitely many multiples of 423. The smallest multiples of 423 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 423 too, since 0 × 423 = 0
423: indeed, 423 is a multiple of itself, since 423 is evenly divisible by 423 (we have 423 / 423 = 1, so the remainder of this division is indeed zero)
846: indeed, 846 = 423 × 2
1 269: indeed, 1 269 = 423 × 3
1 692: indeed, 1 692 = 423 × 4
2 115: indeed, 2 115 = 423 × 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 423). 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 20.567). 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 423

Preceding numbers: …421, 422
Following numbers: 424, 425…

Nearest numbers from 423

Preceding prime number: 421
Following prime number: 431