Which of the following numbers will completely divide 7¹⁰+ 7¹¹+ 7¹²+ 7¹³?

Question: Which of the following numbers will completely divide 7¹⁰ + 7¹¹ + 7¹² + 7¹³?

Solution:
Factors of a number refers to those values that can exactly divide the original number without leaving a remainder. 

7¹⁰ + 7¹¹ + 7¹² + 7¹³ 
= (1 + 7 + 7² + 7³) 7¹⁰
= (1 + 7 + 49 + 343) 7¹⁰
= 400 × 7¹⁰
= 2⁴ × 5² × 7¹⁰
So, the factors are 2, 4, 5, 7, 8, 10 etc.
So, out of given options, required factor = 2 × 7 = 14
∴ 14 will completely divide 7¹⁰ + 7¹¹ + 7¹² + 7¹³.