2014 AMC 10B Problems/Problem 17

Problem 17

What is the greatest power of $2$ that is a factor of $10^{1002} - 4^{501}$ ?

$\textbf{(A) } 2^{1002} \qquad\textbf{(B) } 2^{1003} \qquad\textbf{(C) } 2^{1004} \qquad\textbf{(D) } 2^{1005} \qquad\textbf{(E) }2^{1006}$

We begin by factoring the $2^{1002}$ out. This leaves us with $5^{1002} - 1$ This gives us the final answer of $\textbf{(D) } 2^{1005}$ .

2014 AMC 10B (Problems • Answer Key • Resources)
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