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
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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
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Thank you so much vidhi for help. By the way Have you taken the exam?
No problem
Taking it tomorrow actually