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Question

The greatest prime number that is a divisor of 16,384 is 2 because 16,384 = 2^14. What is the sum of the digits of the greatest prime number that is a divisor of 16,383?

Accepted Answer

We have align* 16383 & = 2^14 - 1 & = ( 2^7 + 1 ) ( 2^7 - 1 ) & = 129 127 align* Since 129 is composite, 127 is the largest prime which can divide 16383. The sum of 127's digits is 1+2+7=: 10.