Question

what is the maximum value of n such that 157! is perfectly divisible by 10^n​

Answer 1

Please see the attachment

Answer 2

Answer:

n = log 157

Step-by-step explanation:

The maximum divisor of 157 will results into 1.

We can therefore rewrite this question as follows :

157/10ⁿ = 1

157 = 10ⁿ

We take logarithms on both sides as:

Log 157 = n log 10

Now the Log of 10 = 1.

Substituting this in the equation above we have that :

Log 157 = n

n = log 157

Therefore the maximum value of n for which 157 is perfectly divisible by 10ⁿ is n = log 157.