Is 538 a prime number?

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

For 538, the answer is: No, 538 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 538) is as follows: 1, 2, 269, 538.

For 538 to be a prime number, it would have been required that 538 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

538 is a multiple of 1
538 is a multiple of 2
538 is a multiple of 269

For 538 to be a prime number, it would have been required that 538 has only two divisors, i.e., itself and 1.

However, 538 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 538 = 2 x 269, where 2 and 269 are both prime numbers.

Is 538 a deficient number?

Yes, 538 is a deficient number, that is to say 538 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 538 without 538 itself (that is 1 + 2 + 269 = 272).

Parity of 538

538 is an even number, because it is evenly divisible by 2: 538 / 2 = 269.

Find out more:

What is an even number?

Is 538 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 538 is about 23.195.

Thus, the square root of 538 is not an integer, and therefore 538 is not a square number.

What is the square number of 538?

The square of a number (here 538) is the result of the product of this number (538) by itself (i.e., 538 × 538); the square of 538 is sometimes called "raising 538 to the power 2", or "538 squared".

The square of 538 is 289 444 because 538 × 538 = 538² = 289 444.

As a consequence, 538 is the square root of 289 444.

Number of digits of 538

538 is a number with 3 digits.

What are the multiples of 538?

The multiples of 538 are all integers evenly divisible by 538, that is all numbers such that the remainder of the division by 538 is zero. There are infinitely many multiples of 538. The smallest multiples of 538 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 538 too, since 0 × 538 = 0
538: indeed, 538 is a multiple of itself, since 538 is evenly divisible by 538 (we have 538 / 538 = 1, so the remainder of this division is indeed zero)
1 076: indeed, 1 076 = 538 × 2
1 614: indeed, 1 614 = 538 × 3
2 152: indeed, 2 152 = 538 × 4
2 690: indeed, 2 690 = 538 × 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 538). 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 23.195). 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 538

Preceding numbers: …536, 537
Following numbers: 539, 540…

Nearest numbers from 538

Preceding prime number: 523
Following prime number: 541