Difference between revisions of "2021 Fall AMC 10B Problems/Problem 8"

Latest revision as of 00:13, 24 November 2021

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-==Problem 8==
+#REDIRECT [[2021_Fall_AMC_12B_Problems/Problem_6]]
-The largest prime factor of <math>16384</math> is <math>2</math>, because <math>16384 = 2^{14}</math>. What is the sum of the digits of the largest prime factor of <math>16383</math>?
-<math>\textbf{(A) }3\qquad\textbf{(B) }7\qquad\textbf{(C) }10\qquad\textbf{(D) }16\qquad\textbf{(E) }22</math>
-==Solution 1==
-We have
-<cmath>16383=16384-1=2^{14}-1=(2^7+1)(2^7-1)=129\cdot127=3\cdot43\cdot127.</cmath>
-Since <math>127</math> is prime, our answer is <math>\boxed{\textbf{(C) }10}</math>.
-~kingofpineapplz