It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 397 401 is not a prime number.
For example, 397 401 can be divided by 3: 397 401 / 3 = 132 467.
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For 397 401 to be a prime number, it would have been required that 397 401 has only two divisors, i.e., itself and 1.
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397 401 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 397 401 is about 630.397.
Thus, the square root of 397 401 is not an integer, and therefore 397 401 is not a square number.
The square of a number (here 397 401) is the result of the product of this number (397 401) by itself (i.e., 397 401 × 397 401); the square of 397 401 is sometimes called "raising 397 401 to the power 2", or "397 401 squared".
The square of 397 401 is 157 927 554 801 because 397 401 × 397 401 = 397 4012 = 157 927 554 801.
As a consequence, 397 401 is the square root of 157 927 554 801.
The multiples of 397 401 are all integers evenly divisible by 397 401, that is all numbers such that the remainder of the division by 397 401 is zero. There are infinitely many multiples of 397 401. The smallest multiples of 397 401 are: