Is 518 a prime number?

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

For 518, the answer is: No, 518 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 518) is as follows: 1, 2, 7, 14, 37, 74, 259, 518.

For 518 to be a prime number, it would have been required that 518 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

518 is a multiple of 1
518 is a multiple of 2
518 is a multiple of 7
518 is a multiple of 14
518 is a multiple of 37
518 is a multiple of 74
518 is a multiple of 259

For 518 to be a prime number, it would have been required that 518 has only two divisors, i.e., itself and 1.

Is 518 a deficient number?

Yes, 518 is a deficient number, that is to say 518 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 518 without 518 itself (that is 1 + 2 + 7 + 14 + 37 + 74 + 259 = 394).

Parity of 518

518 is an even number, because it is evenly divisible by 2: 518 / 2 = 259.

Find out more:

What is an even number?

Is 518 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 518 is about 22.760.

Thus, the square root of 518 is not an integer, and therefore 518 is not a square number.

What is the square number of 518?

The square of a number (here 518) is the result of the product of this number (518) by itself (i.e., 518 × 518); the square of 518 is sometimes called "raising 518 to the power 2", or "518 squared".

The square of 518 is 268 324 because 518 × 518 = 518² = 268 324.

As a consequence, 518 is the square root of 268 324.

Number of digits of 518

518 is a number with 3 digits.

What are the multiples of 518?

The multiples of 518 are all integers evenly divisible by 518, that is all numbers such that the remainder of the division by 518 is zero. There are infinitely many multiples of 518. The smallest multiples of 518 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 518 too, since 0 × 518 = 0
518: indeed, 518 is a multiple of itself, since 518 is evenly divisible by 518 (we have 518 / 518 = 1, so the remainder of this division is indeed zero)
1 036: indeed, 1 036 = 518 × 2
1 554: indeed, 1 554 = 518 × 3
2 072: indeed, 2 072 = 518 × 4
2 590: indeed, 2 590 = 518 × 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 518). 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 22.760). 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 518

Preceding numbers: …516, 517
Following numbers: 519, 520…

Nearest numbers from 518

Preceding prime number: 509
Following prime number: 521