# Generalization of a Factorial Problem

Find the smallest positive integer $$n$$ such that $$n!$$ has $$z$$ zeroes.

Try to generalize the following problem.

Note by Swapnil Das
2 years, 6 months ago

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In the question of Zeroes all around by Akshat Sharda, I generalize the formula as $z = \sum_{i=1}^{\left \lfloor log_5n \right \rfloor} \left \lfloor \frac{n}{5^i} \right \rfloor$

and Akshat Sharda himself provided that the quick approximation is $$n = 4z$$. To find the exact form, it is necessary to add a few more number to this sum to find the right $$n$$

- 2 years, 6 months ago

Oh Yes !!

- 2 years, 6 months ago

Great generalization!

- 2 years, 6 months ago