It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 564 is not a prime number.
For example, 138 564 can be divided by 2: 138 564 / 2 = 69 282.
For 138 564 to be a prime number, it would have been required that 138 564 has only two divisors, i.e., itself and 1.
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138 564 is an even number, because it is evenly divisible by 2: 138 564 / 2 = 69 282.
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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 138 564 is about 372.242.
Thus, the square root of 138 564 is not an integer, and therefore 138 564 is not a square number.
The square of a number (here 138 564) is the result of the product of this number (138 564) by itself (i.e., 138 564 × 138 564); the square of 138 564 is sometimes called "raising 138 564 to the power 2", or "138 564 squared".
The square of 138 564 is 19 199 982 096 because 138 564 × 138 564 = 138 5642 = 19 199 982 096.
As a consequence, 138 564 is the square root of 19 199 982 096.
The multiples of 138 564 are all integers evenly divisible by 138 564, that is all numbers such that the remainder of the division by 138 564 is zero. There are infinitely many multiples of 138 564. The smallest multiples of 138 564 are: