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For how many integer values of \(n\) between 1 and 474 inclusive does the decimal representation of \(\frac{n}{475}\) terminate?

 Jan 19, 2021
 #1
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19  38  57  76  95  114  133  152  171  190  209  228  247  266  285  304  323  342  361  380  399  418  437  456  Total =  24 such integers.

 

Note: ALL of them are multiples of 19

 Jan 19, 2021
 #2
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Hint: Try prime factorizing 475. What is the number without a power? Then, find all of the multiples of [insert number in 475's prime factorization without a power here] from 1 to 474. 

 Jan 21, 2021

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