It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 504 is not a prime number.
For example, 509 504 can be divided by 2: 509 504 / 2 = 254 752.
For 509 504 to be a prime number, it would have been required that 509 504 has only two divisors, i.e., itself and 1.
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509 504 is an even number, because it is evenly divisible by 2: 509 504 / 2 = 254 752.
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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 509 504 is about 713.795.
Thus, the square root of 509 504 is not an integer, and therefore 509 504 is not a square number.
The square of a number (here 509 504) is the result of the product of this number (509 504) by itself (i.e., 509 504 × 509 504); the square of 509 504 is sometimes called "raising 509 504 to the power 2", or "509 504 squared".
The square of 509 504 is 259 594 326 016 because 509 504 × 509 504 = 509 5042 = 259 594 326 016.
As a consequence, 509 504 is the square root of 259 594 326 016.
The multiples of 509 504 are all integers evenly divisible by 509 504, that is all numbers such that the remainder of the division by 509 504 is zero. There are infinitely many multiples of 509 504. The smallest multiples of 509 504 are: