Find the highest power of 9 in 100!Choices:- 24 26 28 30Save AnswerSkip this questionFinish Exam

To find the highest power of 9 in 100!, we first need to understand that 9 is 3^2. So, we need to find the highest power of 3 in 100! and then divide it by 2 because each 9 needs two 3s.

Step 1: Find the highest power of 3 in 100! The formula to find the highest power of a prime p in n! is [n/p] + [n/p^2] + [n/p^3] + .... until p^k > n. Here, [x] denotes the greatest integer less than or equal to x.

So, the highest power of 3 in 100! is [100/3] + [100/9] + [100/27] + [100/81] = 33 + 11 + 3 + 1 = 48.

Step 2: Since 9 is 3^2, we divide the power of 3 by 2. So, the highest power of 9 in 100! is 48/2 = 24.

Therefore, the answer is 24.