It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 262 is not a prime number.
For example, 509 262 can be divided by 2: 509 262 / 2 = 254 631.
For 509 262 to be a prime number, it would have been required that 509 262 has only two divisors, i.e., itself and 1.
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509 262 is an even number, because it is evenly divisible by 2: 509 262 / 2 = 254 631.
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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 509 262 is about 713.626.
Thus, the square root of 509 262 is not an integer, and therefore 509 262 is not a square number.
The square of a number (here 509 262) is the result of the product of this number (509 262) by itself (i.e., 509 262 × 509 262); the square of 509 262 is sometimes called "raising 509 262 to the power 2", or "509 262 squared".
The square of 509 262 is 259 347 784 644 because 509 262 × 509 262 = 509 2622 = 259 347 784 644.
As a consequence, 509 262 is the square root of 259 347 784 644.
The multiples of 509 262 are all integers evenly divisible by 509 262, that is all numbers such that the remainder of the division by 509 262 is zero. There are infinitely many multiples of 509 262. The smallest multiples of 509 262 are: