GWD 06 MATH Q4

GlendaKuo

What is the greatest prime factor of 2^100-2^96?

Can some one tell me how to solve this problem? Thanks.

GlendaKuo

It can also be: 2^100-2^96= 2^96(2^4-1)= 2^96* (16-1)= 2^96*(5*3)
Therefore , the greatest prime factor is 5.

Thanks.

nyc_cfas

2^100-2^96=(2^50-2^48)(2^50+2^48)=(2^25-2^24)(2^25+2^24)(2^50+2^48)

and 2^25-2^24=2^24, 2^25+2^24=3*(2^24), 2^50+2^48=(2*2+1)2^48=5*(2^48),

so, prime factor is 5.