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

 Nov 6, 2021
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199!! [This is double factorial] ==6 666308 670072 953744 411215 006735 034163 324489 389674 388736 363184 954745 922258 576896 518414 625915 283128 424390 474317 708176 893511 841954 015267 176587 405666 801912 441638 268530 971962 511539 459228 515625 (187 digits) = 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, as you can see, is ==49

 Nov 7, 2021

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