Question

The highest power of 12 that completely divides 122! is:

• A. 54
• B. 56
• C. 57
• D. 58

Answer 1

The correct option is D 58

The number of 3's in 122! =40+13+4+1 =58.
The number of 2's in 122!=61+30 +15+7+3+1 =117. The number of $2^2$ s is hence equal to the quotient of $\frac{117}{2}=58$. We have to choose the lower one between 58 and 58. Since both are equal. 58 would be the correct answer. Hence, Option (d) is correct.