请帮我一个笨笨的问题gwd 3-2 m

casualwalk

Q2:

What is the greatest prime factor of 2¹⁰⁰ - 2⁹⁶?

A. 2

B. 3

Answer C. 5

D. 7

E. 11

为何5可以是 prime factor of 2¹⁰⁰ - 2⁹⁶？请解。。感激万分， 谢谢！！！

himba

2^100 - 2^96 = 2^4 * 2^96 - 2^96 = 16 * 2^96 - 2^96 = 15 * 2^96 = 2^96 * 3 * 5.

即质因数分解。