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Determine the largest possible integer n such that 942! is divisible by 80^n.

 Aug 16, 2021
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942! = 2^935 * 3^467 * 5^233 * 7^155.......etc.

 

80 ==2^4  x  5.  Since the exponent of 5 ==233  and 80==2^4  x  5, it therefore follows that the largest possible value of n ==233. So that:

 

942! mod 80^233 ==0 

 Aug 16, 2021

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