If I want to divide $n!$ by $c^x$ but without simply inputting all in a calculator, what would be the best way to do so?
Some example: There are $25!$ atoms on a table. Each second $11^9$ are swept away. How many seconds does it take until all atoms are gone?
EDIT: Looking for a more pen and paper approach.
Best Answer
$$\frac{25!}{11^9}=\frac{25}{11}\frac{24}{11}\frac{23}{11}\frac{22}{11}\frac{21}{11}\frac{20}{11}\frac{19}{11}\frac{18}{11}\frac{17}{11}16!$$
If you calculate all the fractions first, then multiply by 16!, then you might not overflow your calculator. It's still a huge number, 16 digits before the decimal point.