Question

Find the maximum value of n such that $570\times 60\times 30\times 90\times 100\times 500\times 700\times 343\times 720\times 81$ is perfectly divisible by ${30}^n$.

• A. 12
• B. 11
• C. 14
• D. 13

Answer 1

The correct option is B 11

Checking for the number of 2's, 3's and 5's in the given expression you can see that the minimum is for the number of 3's (there are 11 of them while there are 12 5's and definitely more than 11 2's) Hence, option (b) is correct.