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Determine the largest possible integer n such that 942! is divisible by \(80^n\)

 Jun 10, 2022
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942! = 2^935 * 3^467 * 5^233 * 7^155 .............etc.  

 

Since 80 ==2^4   x   5   and since 5 is the largest DISTINCT prime factor of 80, therefore:

 

n==233 or  80^233

 Jun 11, 2022

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