It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 506 209 is not a prime number.
For example, 506 209 can be divided by 11: 506 209 / 11 = 46 019.
For 506 209 to be a prime number, it would have been required that 506 209 has only two divisors, i.e., itself and 1.
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506 209 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 506 209 is about 711.484.
Thus, the square root of 506 209 is not an integer, and therefore 506 209 is not a square number.
The square of a number (here 506 209) is the result of the product of this number (506 209) by itself (i.e., 506 209 × 506 209); the square of 506 209 is sometimes called "raising 506 209 to the power 2", or "506 209 squared".
The square of 506 209 is 256 247 551 681 because 506 209 × 506 209 = 506 2092 = 256 247 551 681.
As a consequence, 506 209 is the square root of 256 247 551 681.
The multiples of 506 209 are all integers evenly divisible by 506 209, that is all numbers such that the remainder of the division by 506 209 is zero. There are infinitely many multiples of 506 209. The smallest multiples of 506 209 are: