It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 506 is not a prime number.
For example, 138 506 can be divided by 2: 138 506 / 2 = 69 253.
For 138 506 to be a prime number, it would have been required that 138 506 has only two divisors, i.e., itself and 1.
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138 506 is an even number, because it is evenly divisible by 2: 138 506 / 2 = 69 253.
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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 138 506 is about 372.164.
Thus, the square root of 138 506 is not an integer, and therefore 138 506 is not a square number.
The square of a number (here 138 506) is the result of the product of this number (138 506) by itself (i.e., 138 506 × 138 506); the square of 138 506 is sometimes called "raising 138 506 to the power 2", or "138 506 squared".
The square of 138 506 is 19 183 912 036 because 138 506 × 138 506 = 138 5062 = 19 183 912 036.
As a consequence, 138 506 is the square root of 19 183 912 036.
The multiples of 138 506 are all integers evenly divisible by 138 506, that is all numbers such that the remainder of the division by 138 506 is zero. There are infinitely many multiples of 138 506. The smallest multiples of 138 506 are: