Question

The number $heta 36$ is divisible by

• A. 2³⁶
• B. 3¹⁸
• C. (12)¹⁷
• D. (24)¹²

Answer 1

Answer: (C)

(12)¹⁷

Answer 2

The index of highest power of 2 that divides $\angle 36$ ie., E₃ ($\angle 36$)

= $\left\lbrack \frac{36}{3} \right\rbrack\mspace{6mu} + \mspace{6mu}\left\lbrack \frac{36}{3^{2}} \right\rbrack\mspace{6mu} + \mspace{6mu}\left\lbrack \frac{36}{3^{3}} \right\rbrack + \left\lbrack \frac{36}{3^{4}} \right\rbrack$ + ...

= 12 + 4 + 1 = 17

Thus, we find that 2³⁴ x 3¹⁷ divides $\angle 36$.

Note that 2³⁶ and 3¹⁸ do not divide$\angle 36$. Also, 24¹²

= (2³ x3)¹² = 2³⁶ x 3¹² does not divide $\angle 36$.

Since 2³⁴ x 3¹⁷ = (2²)¹⁷ x 3¹⁷.

= (2² + 3)¹⁷ = 12¹⁷, therefore, 12¹⁷ divides $\angle 36$.