It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 508 is not a prime number.
For example, 138 508 can be divided by 2: 138 508 / 2 = 69 254.
For 138 508 to be a prime number, it would have been required that 138 508 has only two divisors, i.e., itself and 1.
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138 508 is an even number, because it is evenly divisible by 2: 138 508 / 2 = 69 254.
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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 138 508 is about 372.167.
Thus, the square root of 138 508 is not an integer, and therefore 138 508 is not a square number.
The square of a number (here 138 508) is the result of the product of this number (138 508) by itself (i.e., 138 508 × 138 508); the square of 138 508 is sometimes called "raising 138 508 to the power 2", or "138 508 squared".
The square of 138 508 is 19 184 466 064 because 138 508 × 138 508 = 138 5082 = 19 184 466 064.
As a consequence, 138 508 is the square root of 19 184 466 064.
The multiples of 138 508 are all integers evenly divisible by 138 508, that is all numbers such that the remainder of the division by 138 508 is zero. There are infinitely many multiples of 138 508. The smallest multiples of 138 508 are: