It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 214 is not a prime number.
For example, 509 214 can be divided by 2: 509 214 / 2 = 254 607.
For 509 214 to be a prime number, it would have been required that 509 214 has only two divisors, i.e., itself and 1.
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509 214 is an even number, because it is evenly divisible by 2: 509 214 / 2 = 254 607.
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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 509 214 is about 713.592.
Thus, the square root of 509 214 is not an integer, and therefore 509 214 is not a square number.
The square of a number (here 509 214) is the result of the product of this number (509 214) by itself (i.e., 509 214 × 509 214); the square of 509 214 is sometimes called "raising 509 214 to the power 2", or "509 214 squared".
The square of 509 214 is 259 298 897 796 because 509 214 × 509 214 = 509 2142 = 259 298 897 796.
As a consequence, 509 214 is the square root of 259 298 897 796.
The multiples of 509 214 are all integers evenly divisible by 509 214, that is all numbers such that the remainder of the division by 509 214 is zero. There are infinitely many multiples of 509 214. The smallest multiples of 509 214 are: