2021 AMC 10 B Fall

Complete problem set with solutions and individual problem pages

Problem 8 Easy

The largest prime factor of 16384 is 2 because 16384=2^{14}. What is the sum of the digits of the greatest prime number that is a divisor of 16383 ?(2021 AMC Fall 10B, Question #8)

  • A.

    3

  • B.

    7

  • C.

    10

  • D.

    16

  • E.

    22

Answer:C

We have \begin{aligned} 16383 &=2^{14}-1 \\ &=\left(2^{7}+1\right)\left(2^{7}-1\right) \\ &=129 \cdot 127 \\ &=3 \cdot 43 \cdot 127 . \end{aligned} Therefore, the greatest prime divisor of 16383 is 127 . The sum of its digits is 1+2+7=(\mathbf{C}) 10.

Related Problems
Problem 6 2021 AMC 10 B Fall
Problem 7 2021 AMC 10 B Fall
Problem 9 2021 AMC 10 B Fall
Problem 10 2021 AMC 10 B Fall
Think Academy Powered by ChatGPT