It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 367 is not a prime number.
For example, 509 367 can be divided by 3: 509 367 / 3 = 169 789.
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For 509 367 to be a prime number, it would have been required that 509 367 has only two divisors, i.e., itself and 1.
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509 367 is an odd number, because it is not evenly divisible by 2.
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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 509 367 is about 713.700.
Thus, the square root of 509 367 is not an integer, and therefore 509 367 is not a square number.
The square of a number (here 509 367) is the result of the product of this number (509 367) by itself (i.e., 509 367 × 509 367); the square of 509 367 is sometimes called "raising 509 367 to the power 2", or "509 367 squared".
The square of 509 367 is 259 454 740 689 because 509 367 × 509 367 = 509 3672 = 259 454 740 689.
As a consequence, 509 367 is the square root of 259 454 740 689.
The multiples of 509 367 are all integers evenly divisible by 509 367, that is all numbers such that the remainder of the division by 509 367 is zero. There are infinitely many multiples of 509 367. The smallest multiples of 509 367 are: