It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 034 is not a prime number.
For example, 509 034 can be divided by 2: 509 034 / 2 = 254 517.
For 509 034 to be a prime number, it would have been required that 509 034 has only two divisors, i.e., itself and 1.
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509 034 is an even number, because it is evenly divisible by 2: 509 034 / 2 = 254 517.
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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 509 034 is about 713.466.
Thus, the square root of 509 034 is not an integer, and therefore 509 034 is not a square number.
The square of a number (here 509 034) is the result of the product of this number (509 034) by itself (i.e., 509 034 × 509 034); the square of 509 034 is sometimes called "raising 509 034 to the power 2", or "509 034 squared".
The square of 509 034 is 259 115 613 156 because 509 034 × 509 034 = 509 0342 = 259 115 613 156.
As a consequence, 509 034 is the square root of 259 115 613 156.
The multiples of 509 034 are all integers evenly divisible by 509 034, that is all numbers such that the remainder of the division by 509 034 is zero. There are infinitely many multiples of 509 034. The smallest multiples of 509 034 are: