Is 513 a prime number? What are the divisors of 513?

## Parity of 513

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

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## Is 513 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 513 is about 22.650.

Thus, the square root of 513 is not an integer, and therefore 513 is not a square number.

## What is the square number of 513?

The square of a number (here 513) is the result of the product of this number (513) by itself (i.e., 513 × 513); the square of 513 is sometimes called "raising 513 to the power 2", or "513 squared".

The square of 513 is 263 169 because 513 × 513 = 5132 = 263 169.

As a consequence, 513 is the square root of 263 169.

## Number of digits of 513

513 is a number with 3 digits.

## What are the multiples of 513?

The multiples of 513 are all integers evenly divisible by 513, that is all numbers such that the remainder of the division by 513 is zero. There are infinitely many multiples of 513. The smallest multiples of 513 are:

## 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 513). 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 22.650). 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 513

• Preceding numbers: …511, 512
• Following numbers: 514, 515

### Nearest numbers from 513

• Preceding prime number: 509
• Following prime number: 521
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