It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 413 309 is not a prime number.
For example, 413 309 can be divided by 13: 413 309 / 13 = 31 793.
For 413 309 to be a prime number, it would have been required that 413 309 has only two divisors, i.e., itself and 1.
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413 309 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 413 309 is about 642.891.
Thus, the square root of 413 309 is not an integer, and therefore 413 309 is not a square number.
The square of a number (here 413 309) is the result of the product of this number (413 309) by itself (i.e., 413 309 × 413 309); the square of 413 309 is sometimes called "raising 413 309 to the power 2", or "413 309 squared".
The square of 413 309 is 170 824 329 481 because 413 309 × 413 309 = 413 3092 = 170 824 329 481.
As a consequence, 413 309 is the square root of 170 824 329 481.
The multiples of 413 309 are all integers evenly divisible by 413 309, that is all numbers such that the remainder of the division by 413 309 is zero. There are infinitely many multiples of 413 309. The smallest multiples of 413 309 are: