AMC 10B 2014 Problem 17

Past Contests AMC 10 2014 Part B
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1

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

Answer Choices
A. 2^{1002}
B. 2^{1003}
C. 2^{1004}
D. 2^{1005}
E. 2^{1006}