Question

If 146! is divisible by $6^n$, then find the maximum value of n.

• A. 74
• B. 70
• C. 76
• D. 75

Answer 1

The correct option is B 70

For finding the highest power of 6 that divides 146!, we need to get the number of 3's that would divide 146!. The same can be got by: $\left[\frac{146}{3}\right]+\left[\frac{48}{3}\right]+\left[\frac{16}{3}\right]+\left[\frac{5}{3}\right]=70$