Question

Find the maximum power of 40 in 400!​

Answer 1

Answer:

Look at the prime factors of the numbers from 1 to 100. Collect all the 2's and 3's together.

Here 2 appears 96 times and 3 appears 48 times.

Now come to the question. We need to find the highest power of 12 in 100 factorial.

12=2*2*3

That means to get a power of 12 we need two 2 and one 3.

So we can have minimum(96/2, 48) power of 12

or min(48,48) is 48.

Ans: Highest power of 12 in 100 factorial is 48.