Is 513 a prime number?

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

For 513, the answer is: No, 513 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 513) is as follows: 1, 3, 9, 19, 27, 57, 171, 513.

For 513 to be a prime number, it would have been required that 513 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

513 is a multiple of 1
513 is a multiple of 3
513 is a multiple of 9
513 is a multiple of 19
513 is a multiple of 27
513 is a multiple of 57
513 is a multiple of 171

For 513 to be a prime number, it would have been required that 513 has only two divisors, i.e., itself and 1.

Is 513 a deficient number?

Yes, 513 is a deficient number, that is to say 513 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 513 without 513 itself (that is 1 + 3 + 9 + 19 + 27 + 57 + 171 = 287).

Parity of 513

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

Find out more:

What is an even number?

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:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 513 too, since 0 × 513 = 0
513: indeed, 513 is a multiple of itself, since 513 is evenly divisible by 513 (we have 513 / 513 = 1, so the remainder of this division is indeed zero)
1 026: indeed, 1 026 = 513 × 2
1 539: indeed, 1 539 = 513 × 3
2 052: indeed, 2 052 = 513 × 4
2 565: indeed, 2 565 = 513 × 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 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