It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 538 is not a prime number.
For example, 138 538 can be divided by 2: 138 538 / 2 = 69 269.
For 138 538 to be a prime number, it would have been required that 138 538 has only two divisors, i.e., itself and 1.
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138 538 is an even number, because it is evenly divisible by 2: 138 538 / 2 = 69 269.
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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 138 538 is about 372.207.
Thus, the square root of 138 538 is not an integer, and therefore 138 538 is not a square number.
The square of a number (here 138 538) is the result of the product of this number (138 538) by itself (i.e., 138 538 × 138 538); the square of 138 538 is sometimes called "raising 138 538 to the power 2", or "138 538 squared".
The square of 138 538 is 19 192 777 444 because 138 538 × 138 538 = 138 5382 = 19 192 777 444.
As a consequence, 138 538 is the square root of 19 192 777 444.
The multiples of 138 538 are all integers evenly divisible by 138 538, that is all numbers such that the remainder of the division by 138 538 is zero. There are infinitely many multiples of 138 538. The smallest multiples of 138 538 are: