It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 508 564 is not a prime number.
For example, 508 564 can be divided by 2: 508 564 / 2 = 254 282.
For 508 564 to be a prime number, it would have been required that 508 564 has only two divisors, i.e., itself and 1.
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508 564 is an even number, because it is evenly divisible by 2: 508 564 / 2 = 254 282.
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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 508 564 is about 713.137.
Thus, the square root of 508 564 is not an integer, and therefore 508 564 is not a square number.
The square of a number (here 508 564) is the result of the product of this number (508 564) by itself (i.e., 508 564 × 508 564); the square of 508 564 is sometimes called "raising 508 564 to the power 2", or "508 564 squared".
The square of 508 564 is 258 637 342 096 because 508 564 × 508 564 = 508 5642 = 258 637 342 096.
As a consequence, 508 564 is the square root of 258 637 342 096.
The multiples of 508 564 are all integers evenly divisible by 508 564, that is all numbers such that the remainder of the division by 508 564 is zero. There are infinitely many multiples of 508 564. The smallest multiples of 508 564 are: