It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 708 is not a prime number.
For example, 509 708 can be divided by 2: 509 708 / 2 = 254 854.
For 509 708 to be a prime number, it would have been required that 509 708 has only two divisors, i.e., itself and 1.
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509 708 is an even number, because it is evenly divisible by 2: 509 708 / 2 = 254 854.
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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 509 708 is about 713.938.
Thus, the square root of 509 708 is not an integer, and therefore 509 708 is not a square number.
The square of a number (here 509 708) is the result of the product of this number (509 708) by itself (i.e., 509 708 × 509 708); the square of 509 708 is sometimes called "raising 509 708 to the power 2", or "509 708 squared".
The square of 509 708 is 259 802 245 264 because 509 708 × 509 708 = 509 7082 = 259 802 245 264.
As a consequence, 509 708 is the square root of 259 802 245 264.
The multiples of 509 708 are all integers evenly divisible by 509 708, that is all numbers such that the remainder of the division by 509 708 is zero. There are infinitely many multiples of 509 708. The smallest multiples of 509 708 are: