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

Revision as of 11:35, 23 November 2021

The largest prime factor of $16384$ is $2$ , because $16384 = 2^{14}$ . What is the sum of the digits of the largest prime factor of $16383$ ?

$\textbf{(A) }3\qquad\textbf{(B) }7\qquad\textbf{(C) }10\qquad\textbf{(D) }16\qquad\textbf{(E) }22$

We have

$16383=16384-1=2^{14}-1=(2^7+1)(2^7-1)=129\cdot127=3\cdot43\cdot127.$ Since $127$ is prime, our answer is $\boxed{\textbf{(C) }10}$ .

~kingofpineapplz

2021 Fall AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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 ~kingofpineapplz
+==Solution 2==
 ==See Also==
 {{AMC10 box|year=2021 Fall|ab=B|num-a=9|num-b=7}}
 {{MAA Notice}}