Sequences: Consecutive Integers - Counting Consecutive Multiples within a Range
If $$N$$ is the product of all multiples of 10 between 199 and 301, what is the greatest integer $$m$$ for which $$\frac{N}{10^m}$$ is an integer?
Correct.
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Count how many of the multiples of 10 have more than one 5.
>$$200 = \color{red}{5^2} \times 8$$
>$$250 = 5^2\times 10 = \color{red}{5^3} \times2$$
>$$300 = \color{red}{5^2}\times 12$$
One 5 of each of these is counted in our 11 multiples of 10, but there are 4 additional 5s, which can be used to make 4 additional 10s. All in all, looking at the equation $$11 + 4 = 15$$, there are fifteen 10s in $$N$$. Thus, the greatest possible value of $$m$$ is 15.
Incorrect.
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10
11
13
14
15
