It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 413 007 is not a prime number.
For example, 413 007 can be divided by 3: 413 007 / 3 = 137 669.
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For 413 007 to be a prime number, it would have been required that 413 007 has only two divisors, i.e., itself and 1.
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413 007 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 413 007 is about 642.656.
Thus, the square root of 413 007 is not an integer, and therefore 413 007 is not a square number.
The square of a number (here 413 007) is the result of the product of this number (413 007) by itself (i.e., 413 007 × 413 007); the square of 413 007 is sometimes called "raising 413 007 to the power 2", or "413 007 squared".
The square of 413 007 is 170 574 782 049 because 413 007 × 413 007 = 413 0072 = 170 574 782 049.
As a consequence, 413 007 is the square root of 170 574 782 049.
The multiples of 413 007 are all integers evenly divisible by 413 007, that is all numbers such that the remainder of the division by 413 007 is zero. There are infinitely many multiples of 413 007. The smallest multiples of 413 007 are: