It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 397 657 is not a prime number.
For example, 397 657 can be divided by 13: 397 657 / 13 = 30 589.
For 397 657 to be a prime number, it would have been required that 397 657 has only two divisors, i.e., itself and 1.
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397 657 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 397 657 is about 630.601.
Thus, the square root of 397 657 is not an integer, and therefore 397 657 is not a square number.
The square of a number (here 397 657) is the result of the product of this number (397 657) by itself (i.e., 397 657 × 397 657); the square of 397 657 is sometimes called "raising 397 657 to the power 2", or "397 657 squared".
The square of 397 657 is 158 131 089 649 because 397 657 × 397 657 = 397 6572 = 158 131 089 649.
As a consequence, 397 657 is the square root of 158 131 089 649.
The multiples of 397 657 are all integers evenly divisible by 397 657, that is all numbers such that the remainder of the division by 397 657 is zero. There are infinitely many multiples of 397 657. The smallest multiples of 397 657 are: