Can anyone help me with this problem?

[Kellaybear]

X = 16745797561697357055333354515736371017786!
That's a factorial on the end.


Find the largest n for which (3^n)|X.
"3|12" means "12 is divisible by 3".

Any help is great thanks!

 

[Deleted member 4993]

X = 16745797561697357055333354515736371017786!
That's a factorial on the end.


Find the largest n for which (3^n)|X.
"3|12" means "12 is divisible by 3".

Any help is great thanks!

Hint:

3|3!

3²|6!

3⁴|9!

3⁵|12!

3⁶|15!

3⁸|18!

 

[soroban]

hELLO, Kellaybear!

X = 16745797561697357055333354515736371017786!
That's a factorial on the end.

Find the largest n for which (3^n)|X.
"3|12" means "12 is divisible by 3".

I don't know how they expect us to deal with a 42-digit number,
., . but here is an approach.

Note: is the "greatest integer function".


Calculate the following:

. . \(\displaystyle \begin{array}{cc}\left[\dfrac{x}{3}\right] \\ \left[\dfrac{x}{3^2}\right] \\ \left[\dfrac{x}{3^3}\right] \\ \left[\dfrac{x}{3^4}\right] \\ \vdots \\ \left[\dfrac{x}{3^k}\right] & \text{where }3^k\text{ is the largest power-of-3 that divides }x \end{array}\)


Then add the \(\displaystyle k\) integers.

 

[david3456777]

woah

wow you have some really big smarts sister that is some hard core stuff