It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 462 509 is not a prime number.
For example, 462 509 can be divided by 113: 462 509 / 113 = 4 093.
For 462 509 to be a prime number, it would have been required that 462 509 has only two divisors, i.e., itself and 1.
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462 509 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 462 509 is about 680.080.
Thus, the square root of 462 509 is not an integer, and therefore 462 509 is not a square number.
The square of a number (here 462 509) is the result of the product of this number (462 509) by itself (i.e., 462 509 × 462 509); the square of 462 509 is sometimes called "raising 462 509 to the power 2", or "462 509 squared".
The square of 462 509 is 213 914 575 081 because 462 509 × 462 509 = 462 5092 = 213 914 575 081.
As a consequence, 462 509 is the square root of 213 914 575 081.
The multiples of 462 509 are all integers evenly divisible by 462 509, that is all numbers such that the remainder of the division by 462 509 is zero. There are infinitely many multiples of 462 509. The smallest multiples of 462 509 are: