It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 407 409 is not a prime number.
For example, 407 409 can be divided by 3: 407 409 / 3 = 135 803.
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For 407 409 to be a prime number, it would have been required that 407 409 has only two divisors, i.e., itself and 1.
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407 409 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 407 409 is about 638.286.
Thus, the square root of 407 409 is not an integer, and therefore 407 409 is not a square number.
The square of a number (here 407 409) is the result of the product of this number (407 409) by itself (i.e., 407 409 × 407 409); the square of 407 409 is sometimes called "raising 407 409 to the power 2", or "407 409 squared".
The square of 407 409 is 165 982 093 281 because 407 409 × 407 409 = 407 4092 = 165 982 093 281.
As a consequence, 407 409 is the square root of 165 982 093 281.
The multiples of 407 409 are all integers evenly divisible by 407 409, that is all numbers such that the remainder of the division by 407 409 is zero. There are infinitely many multiples of 407 409. The smallest multiples of 407 409 are: