It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 82 564 is not a prime number.
For example, 82 564 can be divided by 2: 82 564 / 2 = 41 282.
For 82 564 to be a prime number, it would have been required that 82 564 has only two divisors, i.e., itself and 1.
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82 564 is an even number, because it is evenly divisible by 2: 82 564 / 2 = 41 282.
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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 82 564 is about 287.340.
Thus, the square root of 82 564 is not an integer, and therefore 82 564 is not a square number.
The square of a number (here 82 564) is the result of the product of this number (82 564) by itself (i.e., 82 564 × 82 564); the square of 82 564 is sometimes called "raising 82 564 to the power 2", or "82 564 squared".
The square of 82 564 is 6 816 814 096 because 82 564 × 82 564 = 82 5642 = 6 816 814 096.
As a consequence, 82 564 is the square root of 6 816 814 096.
The multiples of 82 564 are all integers evenly divisible by 82 564, that is all numbers such that the remainder of the division by 82 564 is zero. There are infinitely many multiples of 82 564. The smallest multiples of 82 564 are: