It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 107 564 is not a prime number.
For example, 107 564 can be divided by 2: 107 564 / 2 = 53 782.
For 107 564 to be a prime number, it would have been required that 107 564 has only two divisors, i.e., itself and 1.
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107 564 is an even number, because it is evenly divisible by 2: 107 564 / 2 = 53 782.
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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 107 564 is about 327.970.
Thus, the square root of 107 564 is not an integer, and therefore 107 564 is not a square number.
The square of a number (here 107 564) is the result of the product of this number (107 564) by itself (i.e., 107 564 × 107 564); the square of 107 564 is sometimes called "raising 107 564 to the power 2", or "107 564 squared".
The square of 107 564 is 11 570 014 096 because 107 564 × 107 564 = 107 5642 = 11 570 014 096.
As a consequence, 107 564 is the square root of 11 570 014 096.
The multiples of 107 564 are all integers evenly divisible by 107 564, that is all numbers such that the remainder of the division by 107 564 is zero. There are infinitely many multiples of 107 564. The smallest multiples of 107 564 are: