Find the smallest positive integer \(n\) such that \(n!\) has \(z\) zeroes.

Try to generalize the following problem.

Find the smallest positive integer \(n\) such that \(n!\) has \(z\) zeroes.

Try to generalize the following problem.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestIn 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 \(n\) – Kay Xspre · 1 year ago

Log in to reply

– Akshat Sharda · 1 year ago

Oh Yes !!Log in to reply

– Swapnil Das · 1 year ago

Great generalization!Log in to reply