It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 413 421 is not a prime number.
For example, 413 421 can be divided by 3: 413 421 / 3 = 137 807.
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For 413 421 to be a prime number, it would have been required that 413 421 has only two divisors, i.e., itself and 1.
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413 421 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 413 421 is about 642.978.
Thus, the square root of 413 421 is not an integer, and therefore 413 421 is not a square number.
The square of a number (here 413 421) is the result of the product of this number (413 421) by itself (i.e., 413 421 × 413 421); the square of 413 421 is sometimes called "raising 413 421 to the power 2", or "413 421 squared".
The square of 413 421 is 170 916 923 241 because 413 421 × 413 421 = 413 4212 = 170 916 923 241.
As a consequence, 413 421 is the square root of 170 916 923 241.
The multiples of 413 421 are all integers evenly divisible by 413 421, that is all numbers such that the remainder of the division by 413 421 is zero. There are infinitely many multiples of 413 421. The smallest multiples of 413 421 are: