Given that $x$ is a multiple of $23478$, what is the greatest common divisor of $f(x)=(2x+3)(7x+2)(13x+7)(x+13)$ and $x$?

Since 23478 prime factors are = 2 * 3 * 7 * 13 * 43, and the first 4 factors are common to the polynomial f(x)=(2x+3)(7x+2)(13x+7)(x+13), therefore no matter what value x takes, the GCD of the polynomial and x will ALWAYS be = 2 x 3 x 7 x 13 = 546 !!.