How many powers of 900 are in 50! ?

I’m not understand the Question Could you elaborate please?

And also in Greg sir said that there are total 12 5’s in 50!. So when we remove 900 (2^2,3^2,5^2) so we subtract 2 5’s out of 12, so why sir divide 12 by 2?

Take smaller numbers to understand what the question is asking

Rephrased question:

How many powers of 36 are in 10! ?

When you prime factorise 36 you get = 2^2 * 3^2

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 *1 = 2^8 * 3^4 * 5^2 * 7^1

How many times can you divide (2^8 * 3^4 * 5^2 * 7^1) by (2^2 * 3^2)

Dividing once you get (2^6 * 3^2 * 5^2 * 7^1)

Dividing twice you get (2^4 * 3^0 * 5^2 * 7^1)

And then you won’t be able to divide it perfectly any further

So, final answer is **2 times**

The reason for this is because while 2 appeared 8 times in 10!, 3 appeared only 4 times, and you could divide 3^2 from 10! only twice

Coming back to the actual question

900 = 2^2 * 3^2 * 5^2

50! will have plenty of 2s and 3s, so in this case 5 would be the limiting factor

The number of 5’s in 50! = 12

So, how many times can we divide 5^12 by 5^2

Ans. 12/2 = 6

Hey vidhi Thanks for help but Why we divide 3^2 two times in your example. I mean the question is only asked that How many powers are in 10! so after dividing with the denominator number remaining part of the numerator value is not the answer? I mean how many power means how far it can me divided numerator until denominator value is exhausted. Is my strategy is correct or not?

How many powers of 2 are in 24? 24 = 2^3 * 3, so ans. 3

How many times can you divide 24 by 2 perfectly = 3

They both are asking the same thing

Exactly which is why you divide multiple times

Thank you so much vidhi for help. By the way Have you taken the exam?

No problem

Taking it tomorrow actually