GATE ECE 2024 | GA | Question: 5

Question

The greatest prime factor of $\left(3^{199}-3^{196}\right)$ is

• A. $13$
• B. $17$
• C. $3$
• D. $11$

 

Answer 1

We can simplify it, $3^{199}-3^{196} = 3^3 \times3^{196} - 3^{196}$

$\qquad  = 3^{196} (3^3-1) = 3^{196} (27-1) = 26 \times 3^{196} = {\color{red}{13}} \times 2 \times 3^{196}$

So, the greatest prime factor is $13.$

Correct Answer: A

$\textbf{PS:}$ A prime factor is a natural number, other than 1, whose only factors are 1 and itself.

Answer 2

Ans : A : 13

Answer 3

13