It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 409 507 is not a prime number.
For example, 409 507 can be divided by 7: 409 507 / 7 = 58 501.
For 409 507 to be a prime number, it would have been required that 409 507 has only two divisors, i.e., itself and 1.
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409 507 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 409 507 is about 639.927.
Thus, the square root of 409 507 is not an integer, and therefore 409 507 is not a square number.
The square of a number (here 409 507) is the result of the product of this number (409 507) by itself (i.e., 409 507 × 409 507); the square of 409 507 is sometimes called "raising 409 507 to the power 2", or "409 507 squared".
The square of 409 507 is 167 695 983 049 because 409 507 × 409 507 = 409 5072 = 167 695 983 049.
As a consequence, 409 507 is the square root of 167 695 983 049.
The multiples of 409 507 are all integers evenly divisible by 409 507, that is all numbers such that the remainder of the division by 409 507 is zero. There are infinitely many multiples of 409 507. The smallest multiples of 409 507 are: