It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 707 is not a prime number.
For example, 509 707 can be divided by 11: 509 707 / 11 = 46 337.
For 509 707 to be a prime number, it would have been required that 509 707 has only two divisors, i.e., itself and 1.
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509 707 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 509 707 is about 713.938.
Thus, the square root of 509 707 is not an integer, and therefore 509 707 is not a square number.
The square of a number (here 509 707) is the result of the product of this number (509 707) by itself (i.e., 509 707 × 509 707); the square of 509 707 is sometimes called "raising 509 707 to the power 2", or "509 707 squared".
The square of 509 707 is 259 801 225 849 because 509 707 × 509 707 = 509 7072 = 259 801 225 849.
As a consequence, 509 707 is the square root of 259 801 225 849.
The multiples of 509 707 are all integers evenly divisible by 509 707, that is all numbers such that the remainder of the division by 509 707 is zero. There are infinitely many multiples of 509 707. The smallest multiples of 509 707 are: