It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 409 478 is not a prime number.
For example, 409 478 can be divided by 2: 409 478 / 2 = 204 739.
For 409 478 to be a prime number, it would have been required that 409 478 has only two divisors, i.e., itself and 1.
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409 478 is an even number, because it is evenly divisible by 2: 409 478 / 2 = 204 739.
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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 409 478 is about 639.905.
Thus, the square root of 409 478 is not an integer, and therefore 409 478 is not a square number.
The square of a number (here 409 478) is the result of the product of this number (409 478) by itself (i.e., 409 478 × 409 478); the square of 409 478 is sometimes called "raising 409 478 to the power 2", or "409 478 squared".
The square of 409 478 is 167 672 232 484 because 409 478 × 409 478 = 409 4782 = 167 672 232 484.
As a consequence, 409 478 is the square root of 167 672 232 484.
The multiples of 409 478 are all integers evenly divisible by 409 478, that is all numbers such that the remainder of the division by 409 478 is zero. There are infinitely many multiples of 409 478. The smallest multiples of 409 478 are: