Haryana Police Constable Model Paper 3

Given:
The number is $\left({53}^{17}-1\right)$
Concept:
When is n is odd, then $\left({\mathrm{a}}^{\mathrm{n}}-{\mathrm{b}}^{\mathrm{n}}\right)$ is divisible by (a - b)
When n is even, then $\left({\mathrm{a}}^{\mathrm{n}}-{\mathrm{b}}^{\mathrm{n}}\right)$ is divisible by (a - b) and (a + b)
Calculation:
The number is $\left({53}^{17}-1\right)$
Also, we can write this
⇒ $\left({53}^{17}-1^{17}\right)$
Here, n is 17(odd)
Then, the number is must be divisible by
⇒ 53 - 1= 52
Then, the number is also divisible by the factor of 52
Factor 52 is 1, 2, 4, 13, 26, and 52.
∴ The required answer is 13.