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90
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What is the largest integer n such that 3^n is a factor of 1 * 3 * 5 * ... * 97 * 99 * 101 * 103 * ... * 197 * 199?

 Jun 16, 2022
 #1
avatar
+1

6.666308670072953744411215006735034163324489389674388736363184954745922258576896518414625915283128424390474317708176893511841954015267176587405666801912441638268530971962511539459228515625e+186 = 3^49 * 5^25 * 7^16 * 11^10 * 13^9 * 17^6 * 19^5 * 23^4 * 29^3 * 31^3 * 37^3 * 41^2 * 43^2 * 47^2 * 53^2 * 59^2 * 61^2 * 67 * 71 * 73 * 79 * 83 * 89 * 97 * 101 * 103 * 107 * 109 * 113 * 127 * 131 * 137 * 139 * 149 * 151 * 157 * 163 * 167 * 173 * 179 * 181 * 191 * 193 * 197 * 199

 

The largest n==49

 Jun 17, 2022
 #2
avatar+118118 
+1

What is the largest integer n such that 3^n is a factor of 1 * 3 * 5 * ... * 97 * 99 * 101 * 103 * ... * 197 * 199?

 

 

 

199/3 = 66.3333333333333333

199/9 = 22.1111111111111111

199/27 = 7.3703703703703704

199/81 = 2.4567901234567901

 

66+22+7+2 = 97

 

That is what I think.

 Jun 17, 2022

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