It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 164 is not a prime number.
For example, 509 164 can be divided by 2: 509 164 / 2 = 254 582.
For 509 164 to be a prime number, it would have been required that 509 164 has only two divisors, i.e., itself and 1.
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509 164 is an even number, because it is evenly divisible by 2: 509 164 / 2 = 254 582.
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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 509 164 is about 713.557.
Thus, the square root of 509 164 is not an integer, and therefore 509 164 is not a square number.
The square of a number (here 509 164) is the result of the product of this number (509 164) by itself (i.e., 509 164 × 509 164); the square of 509 164 is sometimes called "raising 509 164 to the power 2", or "509 164 squared".
The square of 509 164 is 259 247 978 896 because 509 164 × 509 164 = 509 1642 = 259 247 978 896.
As a consequence, 509 164 is the square root of 259 247 978 896.
The multiples of 509 164 are all integers evenly divisible by 509 164, that is all numbers such that the remainder of the division by 509 164 is zero. There are infinitely many multiples of 509 164. The smallest multiples of 509 164 are: