It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 397 397 is not a prime number.
For example, 397 397 can be divided by 7: 397 397 / 7 = 56 771.
For 397 397 to be a prime number, it would have been required that 397 397 has only two divisors, i.e., itself and 1.
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397 397 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 397 397 is about 630.394.
Thus, the square root of 397 397 is not an integer, and therefore 397 397 is not a square number.
The square of a number (here 397 397) is the result of the product of this number (397 397) by itself (i.e., 397 397 × 397 397); the square of 397 397 is sometimes called "raising 397 397 to the power 2", or "397 397 squared".
The square of 397 397 is 157 924 375 609 because 397 397 × 397 397 = 397 3972 = 157 924 375 609.
As a consequence, 397 397 is the square root of 157 924 375 609.
The multiples of 397 397 are all integers evenly divisible by 397 397, that is all numbers such that the remainder of the division by 397 397 is zero. There are infinitely many multiples of 397 397. The smallest multiples of 397 397 are: