I need more explanation on how to solve-- How many 4s are there in 50!
I found the number of 2 raised to power 1 25.
I got stuck with 2 raised to power 2. I did 50-4 = 46, so (46/4) +1, but that turns out to be a decimal. How to proceed?
I have had no issues solving similar questions like How many 3s are there in 30!.
or How many 5s are there in 50! coz at no point the cal turns out to be a decimal.
Start with 4, not 2.
Could you please elaborate more?
Even if I start with 4, it would still be 50-4 = 46, so (46/4) +1. That would be a decimal.
I’d approach this a bit differently.
How many multiples of 4 are there up to 50? That’s 12 - 4, 8, 12, 16, … up to 48.
Then, consider multiples of 16.
It’s a bit different than what Greg talks about in the class. He starts with two.
@gregmat Could you please elaborate on this if you get a chance?
Thanks
Once you find the number of 2s from 1-50, to find the number of 4s, and then number of 8s, and then the number of 16s, and then the number of 32s, just keep dividing by 2 (keeping the quotient only).
For example, imagine we have 100!/2^x, and we’re trying to find the number of twos. First, find the number of 2s in 1-100.
That’s 50.
Then just keep dividing by 2. 50/2 = 25
So we have 25 fours.
Then divide by two again: 25/2 = 12 (remember keep the quotient only)… This is the number of eights.
so you get:
50…25…12…6…3…1…0…0…0…0
Just add together
so basically there are 97 2s in 100 factorial and number of 4s will be the quotient of 97/2 which is 48
Is my understanding correct here ? Please reply
@gregmat Please confirm if my understanding is correct
