It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 523 is not a prime number.
For example, 138 523 can be divided by 7: 138 523 / 7 = 19 789.
For 138 523 to be a prime number, it would have been required that 138 523 has only two divisors, i.e., itself and 1.
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138 523 is an odd number, because it is not evenly divisible by 2.
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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 138 523 is about 372.187.
Thus, the square root of 138 523 is not an integer, and therefore 138 523 is not a square number.
The square of a number (here 138 523) is the result of the product of this number (138 523) by itself (i.e., 138 523 × 138 523); the square of 138 523 is sometimes called "raising 138 523 to the power 2", or "138 523 squared".
The square of 138 523 is 19 188 621 529 because 138 523 × 138 523 = 138 5232 = 19 188 621 529.
As a consequence, 138 523 is the square root of 19 188 621 529.
The multiples of 138 523 are all integers evenly divisible by 138 523, that is all numbers such that the remainder of the division by 138 523 is zero. There are infinitely many multiples of 138 523. The smallest multiples of 138 523 are: