It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 644 is not a prime number.
For example, 509 644 can be divided by 2: 509 644 / 2 = 254 822.
For 509 644 to be a prime number, it would have been required that 509 644 has only two divisors, i.e., itself and 1.
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509 644 is an even number, because it is evenly divisible by 2: 509 644 / 2 = 254 822.
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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 509 644 is about 713.894.
Thus, the square root of 509 644 is not an integer, and therefore 509 644 is not a square number.
The square of a number (here 509 644) is the result of the product of this number (509 644) by itself (i.e., 509 644 × 509 644); the square of 509 644 is sometimes called "raising 509 644 to the power 2", or "509 644 squared".
The square of 509 644 is 259 737 006 736 because 509 644 × 509 644 = 509 6442 = 259 737 006 736.
As a consequence, 509 644 is the square root of 259 737 006 736.
The multiples of 509 644 are all integers evenly divisible by 509 644, that is all numbers such that the remainder of the division by 509 644 is zero. There are infinitely many multiples of 509 644. The smallest multiples of 509 644 are: