Problem:
The largest prime factor of 16384 is 2, because 16384=214. What is the sum of the digits of the largest prime factor of 16383?
Answer Choices:
A. 3
B. 7
C. 10
D. 16
E. 22
Solution:
We have
16383=214−1=(27+1)(27−1)=129⋅127
Since 129 is composite, 127 is the largest prime which can divide 16383. The sum of 127’s digits is 1+2+7=(C) 10.
The problems on this page are the property of the MAA's American Mathematics Competitions