It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 261 is not a prime number.
For example, 509 261 can be divided by 41: 509 261 / 41 = 12 421.
For 509 261 to be a prime number, it would have been required that 509 261 has only two divisors, i.e., itself and 1.
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509 261 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 509 261 is about 713.625.
Thus, the square root of 509 261 is not an integer, and therefore 509 261 is not a square number.
The square of a number (here 509 261) is the result of the product of this number (509 261) by itself (i.e., 509 261 × 509 261); the square of 509 261 is sometimes called "raising 509 261 to the power 2", or "509 261 squared".
The square of 509 261 is 259 346 766 121 because 509 261 × 509 261 = 509 2612 = 259 346 766 121.
As a consequence, 509 261 is the square root of 259 346 766 121.
The multiples of 509 261 are all integers evenly divisible by 509 261, that is all numbers such that the remainder of the division by 509 261 is zero. There are infinitely many multiples of 509 261. The smallest multiples of 509 261 are: