It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 409 309 is not a prime number.
For example, 409 309 can be divided by 17: 409 309 / 17 = 24 077.
For 409 309 to be a prime number, it would have been required that 409 309 has only two divisors, i.e., itself and 1.
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409 309 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 409 309 is about 639.773.
Thus, the square root of 409 309 is not an integer, and therefore 409 309 is not a square number.
The square of a number (here 409 309) is the result of the product of this number (409 309) by itself (i.e., 409 309 × 409 309); the square of 409 309 is sometimes called "raising 409 309 to the power 2", or "409 309 squared".
The square of 409 309 is 167 533 857 481 because 409 309 × 409 309 = 409 3092 = 167 533 857 481.
As a consequence, 409 309 is the square root of 167 533 857 481.
The multiples of 409 309 are all integers evenly divisible by 409 309, that is all numbers such that the remainder of the division by 409 309 is zero. There are infinitely many multiples of 409 309. The smallest multiples of 409 309 are: