1. ## prime numbers

What is the greatest prime factor of 3^100-3^97?

My method:

$3^{100}-3^{97}=3^{97}(3^{3}-1)=3^{97}(26)$. 13 is a factor of 26 and so 13 is the greatest prime factor.

Can I deduce that from what I just did?

2. Originally Posted by sfspitfire23
What is the greatest prime factor of 3^100-3^97?

My method:

$3^{100}-3^{97}=3^{97}(3^{3}-1)=3^{97}(26)$. 13 is a factor of 26 and so 13 is the greatest prime factor.

Can I deduce that from what I just did?
Yes, 3, 13 and 2 are the prime factors.