It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 38 564 is not a prime number.
For example, 38 564 can be divided by 2: 38 564 / 2 = 19 282.
For 38 564 to be a prime number, it would have been required that 38 564 has only two divisors, i.e., itself and 1.
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38 564 is an even number, because it is evenly divisible by 2: 38 564 / 2 = 19 282.
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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 38 564 is about 196.377.
Thus, the square root of 38 564 is not an integer, and therefore 38 564 is not a square number.
The square of a number (here 38 564) is the result of the product of this number (38 564) by itself (i.e., 38 564 × 38 564); the square of 38 564 is sometimes called "raising 38 564 to the power 2", or "38 564 squared".
The square of 38 564 is 1 487 182 096 because 38 564 × 38 564 = 38 5642 = 1 487 182 096.
As a consequence, 38 564 is the square root of 1 487 182 096.
The multiples of 38 564 are all integers evenly divisible by 38 564, that is all numbers such that the remainder of the division by 38 564 is zero. There are infinitely many multiples of 38 564. The smallest multiples of 38 564 are: