It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 209 309 is not a prime number.
For example, 209 309 can be divided by 37: 209 309 / 37 = 5 657.
For 209 309 to be a prime number, it would have been required that 209 309 has only two divisors, i.e., itself and 1.
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209 309 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 209 309 is about 457.503.
Thus, the square root of 209 309 is not an integer, and therefore 209 309 is not a square number.
The square of a number (here 209 309) is the result of the product of this number (209 309) by itself (i.e., 209 309 × 209 309); the square of 209 309 is sometimes called "raising 209 309 to the power 2", or "209 309 squared".
The square of 209 309 is 43 810 257 481 because 209 309 × 209 309 = 209 3092 = 43 810 257 481.
As a consequence, 209 309 is the square root of 43 810 257 481.
The multiples of 209 309 are all integers evenly divisible by 209 309, that is all numbers such that the remainder of the division by 209 309 is zero. There are infinitely many multiples of 209 309. The smallest multiples of 209 309 are: