Question 87

The largest power of 3 that divides $$(20)!$$ is

Solution

The largest power of 3 that divides $$(20)!$$ = Sum of quotients of {$$\frac{20}{3}, \frac{20}{3^2}, \frac{20}{3^3},$$....}

= Sum of quotients of $$\frac{20}{3},\frac{20}{9},\frac{20}{27},....$$

= 6 + 2 + 0 + 0 +.....

= 8

$$\therefore\ $$The largest power of 3 that divides $$(20)!$$ is $$3^8$$

Hence, the correct answer is Option D

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