Is 516 a prime number?

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

For 516, the answer is: No, 516 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 516) is as follows: 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516.

For 516 to be a prime number, it would have been required that 516 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

516 is a multiple of 1
516 is a multiple of 2
516 is a multiple of 3
516 is a multiple of 4
516 is a multiple of 6
516 is a multiple of 12
516 is a multiple of 43
516 is a multiple of 86
516 is a multiple of 129
516 is a multiple of 172
516 is a multiple of 258

For 516 to be a prime number, it would have been required that 516 has only two divisors, i.e., itself and 1.

Is 516 a deficient number?

No, 516 is not a deficient number: to be deficient, 516 should have been such that 516 is larger than the sum of its proper divisors, i.e., the divisors of 516 without 516 itself (that is 1 + 2 + 3 + 4 + 6 + 12 + 43 + 86 + 129 + 172 + 258 = 716).

In fact, 516 is an abundant number; 516 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 12 + 43 + 86 + 129 + 172 + 258 = 716). The smallest abundant number is 12.

Parity of 516

516 is an even number, because it is evenly divisible by 2: 516 / 2 = 258.

Find out more:

What is an even number?

Is 516 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 516 is about 22.716.

Thus, the square root of 516 is not an integer, and therefore 516 is not a square number.

What is the square number of 516?

The square of a number (here 516) is the result of the product of this number (516) by itself (i.e., 516 × 516); the square of 516 is sometimes called "raising 516 to the power 2", or "516 squared".

The square of 516 is 266 256 because 516 × 516 = 516² = 266 256.

As a consequence, 516 is the square root of 266 256.

Number of digits of 516

516 is a number with 3 digits.

What are the multiples of 516?

The multiples of 516 are all integers evenly divisible by 516, that is all numbers such that the remainder of the division by 516 is zero. There are infinitely many multiples of 516. The smallest multiples of 516 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 516 too, since 0 × 516 = 0
516: indeed, 516 is a multiple of itself, since 516 is evenly divisible by 516 (we have 516 / 516 = 1, so the remainder of this division is indeed zero)
1 032: indeed, 1 032 = 516 × 2
1 548: indeed, 1 548 = 516 × 3
2 064: indeed, 2 064 = 516 × 4
2 580: indeed, 2 580 = 516 × 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 516). 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 22.716). 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 516

Preceding numbers: …514, 515
Following numbers: 517, 518…

Nearest numbers from 516

Preceding prime number: 509
Following prime number: 521