It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 397 is not a prime number.
For example, 137 397 can be divided by 3: 137 397 / 3 = 45 799.
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For 137 397 to be a prime number, it would have been required that 137 397 has only two divisors, i.e., itself and 1.
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137 397 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 137 397 is about 370.671.
Thus, the square root of 137 397 is not an integer, and therefore 137 397 is not a square number.
The square of a number (here 137 397) is the result of the product of this number (137 397) by itself (i.e., 137 397 × 137 397); the square of 137 397 is sometimes called "raising 137 397 to the power 2", or "137 397 squared".
The square of 137 397 is 18 877 935 609 because 137 397 × 137 397 = 137 3972 = 18 877 935 609.
As a consequence, 137 397 is the square root of 18 877 935 609.
The multiples of 137 397 are all integers evenly divisible by 137 397, that is all numbers such that the remainder of the division by 137 397 is zero. There are infinitely many multiples of 137 397. The smallest multiples of 137 397 are: