It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 202 is not a prime number.
For example, 509 202 can be divided by 2: 509 202 / 2 = 254 601.
For 509 202 to be a prime number, it would have been required that 509 202 has only two divisors, i.e., itself and 1.
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509 202 is an even number, because it is evenly divisible by 2: 509 202 / 2 = 254 601.
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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 509 202 is about 713.584.
Thus, the square root of 509 202 is not an integer, and therefore 509 202 is not a square number.
The square of a number (here 509 202) is the result of the product of this number (509 202) by itself (i.e., 509 202 × 509 202); the square of 509 202 is sometimes called "raising 509 202 to the power 2", or "509 202 squared".
The square of 509 202 is 259 286 676 804 because 509 202 × 509 202 = 509 2022 = 259 286 676 804.
As a consequence, 509 202 is the square root of 259 286 676 804.
The multiples of 509 202 are all integers evenly divisible by 509 202, that is all numbers such that the remainder of the division by 509 202 is zero. There are infinitely many multiples of 509 202. The smallest multiples of 509 202 are: