It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 421 413 is not a prime number.
For example, 421 413 can be divided by 3: 421 413 / 3 = 140 471.
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For 421 413 to be a prime number, it would have been required that 421 413 has only two divisors, i.e., itself and 1.
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421 413 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 421 413 is about 649.163.
Thus, the square root of 421 413 is not an integer, and therefore 421 413 is not a square number.
The square of a number (here 421 413) is the result of the product of this number (421 413) by itself (i.e., 421 413 × 421 413); the square of 421 413 is sometimes called "raising 421 413 to the power 2", or "421 413 squared".
The square of 421 413 is 177 588 916 569 because 421 413 × 421 413 = 421 4132 = 177 588 916 569.
As a consequence, 421 413 is the square root of 177 588 916 569.
The multiples of 421 413 are all integers evenly divisible by 421 413, that is all numbers such that the remainder of the division by 421 413 is zero. There are infinitely many multiples of 421 413. The smallest multiples of 421 413 are: