Is 424 a prime number?

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

For 424, the answer is: No, 424 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 424) is as follows: 1, 2, 4, 8, 53, 106, 212, 424.

For 424 to be a prime number, it would have been required that 424 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

424 is a multiple of 1
424 is a multiple of 2
424 is a multiple of 4
424 is a multiple of 8
424 is a multiple of 53
424 is a multiple of 106
424 is a multiple of 212

For 424 to be a prime number, it would have been required that 424 has only two divisors, i.e., itself and 1.

Is 424 a deficient number?

Yes, 424 is a deficient number, that is to say 424 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 424 without 424 itself (that is 1 + 2 + 4 + 8 + 53 + 106 + 212 = 386).

Parity of 424

424 is an even number, because it is evenly divisible by 2: 424 / 2 = 212.

Find out more:

What is an even number?

Is 424 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 424 is about 20.591.

Thus, the square root of 424 is not an integer, and therefore 424 is not a square number.

What is the square number of 424?

The square of a number (here 424) is the result of the product of this number (424) by itself (i.e., 424 × 424); the square of 424 is sometimes called "raising 424 to the power 2", or "424 squared".

The square of 424 is 179 776 because 424 × 424 = 424² = 179 776.

As a consequence, 424 is the square root of 179 776.

Number of digits of 424

424 is a number with 3 digits.

What are the multiples of 424?

The multiples of 424 are all integers evenly divisible by 424, that is all numbers such that the remainder of the division by 424 is zero. There are infinitely many multiples of 424. The smallest multiples of 424 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 424 too, since 0 × 424 = 0
424: indeed, 424 is a multiple of itself, since 424 is evenly divisible by 424 (we have 424 / 424 = 1, so the remainder of this division is indeed zero)
848: indeed, 848 = 424 × 2
1 272: indeed, 1 272 = 424 × 3
1 696: indeed, 1 696 = 424 × 4
2 120: indeed, 2 120 = 424 × 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 424). 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 20.591). 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 424

Preceding numbers: …422, 423
Following numbers: 425, 426…

Nearest numbers from 424

Preceding prime number: 421
Following prime number: 431