arithmetic - Division with 4 digit number in denominator

I've got a question in my task sheet. The question is as follows.

$$\frac{43\cdot93\cdot47\cdot97}{3007}=X$$

Find the exact value of $X$. I've tried a lot, but couldn't find easier way to do it without calculator, which of course, is not allowed in exam. There are no options, they're just asking the value of $X$.

Would love if someone could help to give Method to solve the problem. As I said, I know how to solve above problem with the help of calculators and I've already found the factorization with help of calc, but no luck in manual mode. :(

Thanks in advance. :)

Answer

HINT $\ \rm mod \; 97\!: \: 100 \;\equiv\; 3$

Hence $\; 3007 \;\equiv\; 30 \cdot 100 + 7$

$\quad\quad\quad\quad\quad\quad\;\; \;\equiv\; 30 \:\;\cdot\;\: 3 \;\: + \; 7 \;$

$\quad\quad\quad\quad\quad\quad\;\; \;\equiv\; 0$

I.e. cast out 97's in analogy to cast out nines. See also here where I discuss casting out 91's.