It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 301 is not a prime number.
For example, 138 301 can be divided by 19: 138 301 / 19 = 7 279.
For 138 301 to be a prime number, it would have been required that 138 301 has only two divisors, i.e., itself and 1.
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138 301 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 138 301 is about 371.888.
Thus, the square root of 138 301 is not an integer, and therefore 138 301 is not a square number.
The square of a number (here 138 301) is the result of the product of this number (138 301) by itself (i.e., 138 301 × 138 301); the square of 138 301 is sometimes called "raising 138 301 to the power 2", or "138 301 squared".
The square of 138 301 is 19 127 166 601 because 138 301 × 138 301 = 138 3012 = 19 127 166 601.
As a consequence, 138 301 is the square root of 19 127 166 601.
The multiples of 138 301 are all integers evenly divisible by 138 301, that is all numbers such that the remainder of the division by 138 301 is zero. There are infinitely many multiples of 138 301. The smallest multiples of 138 301 are: