Is 564 a prime number?

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

For 564, the answer is: No, 564 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 564) is as follows: 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564.

For 564 to be a prime number, it would have been required that 564 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

564 is a multiple of 1
564 is a multiple of 2
564 is a multiple of 3
564 is a multiple of 4
564 is a multiple of 6
564 is a multiple of 12
564 is a multiple of 47
564 is a multiple of 94
564 is a multiple of 141
564 is a multiple of 188
564 is a multiple of 282

For 564 to be a prime number, it would have been required that 564 has only two divisors, i.e., itself and 1.

Is 564 a deficient number?

No, 564 is not a deficient number: to be deficient, 564 should have been such that 564 is larger than the sum of its proper divisors, i.e., the divisors of 564 without 564 itself (that is 1 + 2 + 3 + 4 + 6 + 12 + 47 + 94 + 141 + 188 + 282 = 780).

In fact, 564 is an abundant number; 564 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 12 + 47 + 94 + 141 + 188 + 282 = 780). The smallest abundant number is 12.

Parity of 564

564 is an even number, because it is evenly divisible by 2: 564 / 2 = 282.

Find out more:

What is an even number?

Is 564 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 564 is about 23.749.

Thus, the square root of 564 is not an integer, and therefore 564 is not a square number.

What is the square number of 564?

The square of a number (here 564) is the result of the product of this number (564) by itself (i.e., 564 × 564); the square of 564 is sometimes called "raising 564 to the power 2", or "564 squared".

The square of 564 is 318 096 because 564 × 564 = 564² = 318 096.

As a consequence, 564 is the square root of 318 096.

Number of digits of 564

564 is a number with 3 digits.

What are the multiples of 564?

The multiples of 564 are all integers evenly divisible by 564, that is all numbers such that the remainder of the division by 564 is zero. There are infinitely many multiples of 564. The smallest multiples of 564 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 564 too, since 0 × 564 = 0
564: indeed, 564 is a multiple of itself, since 564 is evenly divisible by 564 (we have 564 / 564 = 1, so the remainder of this division is indeed zero)
1 128: indeed, 1 128 = 564 × 2
1 692: indeed, 1 692 = 564 × 3
2 256: indeed, 2 256 = 564 × 4
2 820: indeed, 2 820 = 564 × 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 564). 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 23.749). 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 564

Preceding numbers: …562, 563
Following numbers: 565, 566…

Nearest numbers from 564

Preceding prime number: 563
Following prime number: 569