It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 709 is not a prime number.
For example, 509 709 can be divided by 3: 509 709 / 3 = 169 903.
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For 509 709 to be a prime number, it would have been required that 509 709 has only two divisors, i.e., itself and 1.
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509 709 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 509 709 is about 713.939.
Thus, the square root of 509 709 is not an integer, and therefore 509 709 is not a square number.
The square of a number (here 509 709) is the result of the product of this number (509 709) by itself (i.e., 509 709 × 509 709); the square of 509 709 is sometimes called "raising 509 709 to the power 2", or "509 709 squared".
The square of 509 709 is 259 803 264 681 because 509 709 × 509 709 = 509 7092 = 259 803 264 681.
As a consequence, 509 709 is the square root of 259 803 264 681.
The multiples of 509 709 are all integers evenly divisible by 509 709, that is all numbers such that the remainder of the division by 509 709 is zero. There are infinitely many multiples of 509 709. The smallest multiples of 509 709 are: