It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 508 414 is not a prime number.
For example, 508 414 can be divided by 2: 508 414 / 2 = 254 207.
For 508 414 to be a prime number, it would have been required that 508 414 has only two divisors, i.e., itself and 1.
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508 414 is an even number, because it is evenly divisible by 2: 508 414 / 2 = 254 207.
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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 508 414 is about 713.032.
Thus, the square root of 508 414 is not an integer, and therefore 508 414 is not a square number.
The square of a number (here 508 414) is the result of the product of this number (508 414) by itself (i.e., 508 414 × 508 414); the square of 508 414 is sometimes called "raising 508 414 to the power 2", or "508 414 squared".
The square of 508 414 is 258 484 795 396 because 508 414 × 508 414 = 508 4142 = 258 484 795 396.
As a consequence, 508 414 is the square root of 258 484 795 396.
The multiples of 508 414 are all integers evenly divisible by 508 414, that is all numbers such that the remainder of the division by 508 414 is zero. There are infinitely many multiples of 508 414. The smallest multiples of 508 414 are: