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}

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}