It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 397 is not a prime number.
For example, 138 397 can be divided by 7: 138 397 / 7 = 19 771.
For 138 397 to be a prime number, it would have been required that 138 397 has only two divisors, i.e., itself and 1.
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138 397 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 138 397 is about 372.017.
Thus, the square root of 138 397 is not an integer, and therefore 138 397 is not a square number.
The square of a number (here 138 397) is the result of the product of this number (138 397) by itself (i.e., 138 397 × 138 397); the square of 138 397 is sometimes called "raising 138 397 to the power 2", or "138 397 squared".
The square of 138 397 is 19 153 729 609 because 138 397 × 138 397 = 138 3972 = 19 153 729 609.
As a consequence, 138 397 is the square root of 19 153 729 609.
The multiples of 138 397 are all integers evenly divisible by 138 397, that is all numbers such that the remainder of the division by 138 397 is zero. There are infinitely many multiples of 138 397. The smallest multiples of 138 397 are: