Which of the following numbers divides (3^25 + 3^26 + 3^27 + 3^28) exactly?

Given data

• Expression: 3^25 + 3^26 + 3^27 + 3^28

Concept / Approach

• Factor out the smallest power to reveal a simple integer factor.

Step-by-step calculation

3^25 + 3^26 + 3^27 + 3^28 = 3^25(1 + 3 + 3^2 + 3^3)= 3^25(1 + 3 + 9 + 27) = 3^25 × 40Therefore, any divisor of 40 divides the entire sum; in particular, 40 divides it.

Why others do not

7, 11, 13 are not factors of 40 and do not divide any power of 3, hence they do not necessarily divide the expression.

Final Answer

Divisible by 40.