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

 Feb 20, 2021
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The largest integer, n, is when n =233. 

 

Since  80 = 2^4 * 5  and  942! === 2^935 * 3^467 * 5^233 * 7^155 ........etc.

 

Therefore: 942! mod 80^233 ==0.

 Feb 20, 2021

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