It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 507 564 is not a prime number.
For example, 507 564 can be divided by 2: 507 564 / 2 = 253 782.
For 507 564 to be a prime number, it would have been required that 507 564 has only two divisors, i.e., itself and 1.
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507 564 is an even number, because it is evenly divisible by 2: 507 564 / 2 = 253 782.
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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 507 564 is about 712.435.
Thus, the square root of 507 564 is not an integer, and therefore 507 564 is not a square number.
The square of a number (here 507 564) is the result of the product of this number (507 564) by itself (i.e., 507 564 × 507 564); the square of 507 564 is sometimes called "raising 507 564 to the power 2", or "507 564 squared".
The square of 507 564 is 257 621 214 096 because 507 564 × 507 564 = 507 5642 = 257 621 214 096.
As a consequence, 507 564 is the square root of 257 621 214 096.
The multiples of 507 564 are all integers evenly divisible by 507 564, that is all numbers such that the remainder of the division by 507 564 is zero. There are infinitely many multiples of 507 564. The smallest multiples of 507 564 are: