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What is the greatest integer k such that 80! is divisible by 4^k?

 

\(\phantom{45^k}\) 

 Jul 9, 2022
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80!= 2^78 * 3^36 * 5^19 * 7^12 * 11^7 * 13^6 * 17^4 * 19^4 * 23^3 * 29^2 * 31^2 * 37^2 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71 * 73 * 79

 

k==78 / 2 ==39 ==4^39

 Jul 9, 2022

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