It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 413 397 is not a prime number.
For example, 413 397 can be divided by 3: 413 397 / 3 = 137 799.
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For 413 397 to be a prime number, it would have been required that 413 397 has only two divisors, i.e., itself and 1.
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413 397 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 413 397 is about 642.960.
Thus, the square root of 413 397 is not an integer, and therefore 413 397 is not a square number.
The square of a number (here 413 397) is the result of the product of this number (413 397) by itself (i.e., 413 397 × 413 397); the square of 413 397 is sometimes called "raising 413 397 to the power 2", or "413 397 squared".
The square of 413 397 is 170 897 079 609 because 413 397 × 413 397 = 413 3972 = 170 897 079 609.
As a consequence, 413 397 is the square root of 170 897 079 609.
The multiples of 413 397 are all integers evenly divisible by 413 397, that is all numbers such that the remainder of the division by 413 397 is zero. There are infinitely many multiples of 413 397. The smallest multiples of 413 397 are: