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17 Aug 2019, 07:19
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I have two questions on the topic, the first relates to finding the number of powers of a prime number p in n! and the second relates to finding the number of powers of a non-prime in n!.
1) According to the GMAT Club Math book, the formula is:
n/p + n/(p^2) + n/(p^3).. until (p^x)<n
However, this doesn't seem to work for the powers of 2 in 4! ?
We know that 4! = 4*3*2*1 = (2*2)*3*2*1 = (2^3)*3, so the answer we get via the above formula should be 3. However, if we go ahead and do this:
n/p = 4/2 = 2? If I take it one term further 4/(2^2) then we get 4/2 + 4/(2^2) = 2+1=3, which is indeed the right answer but this extra term violates the condition (p^x)<n ? The only thing I can think of is that p^x should be less than or equal to n and not just less than?
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2) The second question I have is regarding this (also from the GMAT Math Book)
I understand everything here apart from the last sentence. Can someone explain?
1) According to the GMAT Club Math book, the formula is:
n/p + n/(p^2) + n/(p^3).. until (p^x)<n
However, this doesn't seem to work for the powers of 2 in 4! ?
We know that 4! = 4*3*2*1 = (2*2)*3*2*1 = (2^3)*3, so the answer we get via the above formula should be 3. However, if we go ahead and do this:
n/p = 4/2 = 2? If I take it one term further 4/(2^2) then we get 4/2 + 4/(2^2) = 2+1=3, which is indeed the right answer but this extra term violates the condition (p^x)<n ? The only thing I can think of is that p^x should be less than or equal to n and not just less than?
---
2) The second question I have is regarding this (also from the GMAT Math Book)
I understand everything here apart from the last sentence. Can someone explain?
vijyband99
Joined: 25 Mar 2017
Last visit: 23 Oct 2025
Posts: 21
Given Kudos: 111
Location: India
Schools: IIMA PGPX"20 ISB '20 IIMC PGPEX"20 Kellogg '21 Marshall '21 Ross '21 Sloan '21 Smeal'21 IIMB
GMAT 1: 650 Q49 V31
GMAT 2: 700 Q47 V39
GPA: 3.1
Products:
Schools: IIMA PGPX"20 ISB '20 IIMC PGPEX"20 Kellogg '21 Marshall '21 Ross '21 Sloan '21 Smeal'21 IIMB
GMAT 2: 700 Q47 V39
Posts: 21
20 Aug 2019, 22:30
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It means that to find how many times can 900 divide into 50!..to find this we had figured out the prime factors of 900 those are 2,3and 5 in their square...so the last statement talks of 2,3&5 being represented twice (square power of these prime numbers). Minimum power out of 2,3&5 is for 5 which has 12th power in 50!. So power of 5 will limit the power of 900 that will be represented in 50! We are looking for square of 5 so 5 to the power 12 gives us 6power of 5 square. Hence our answer is 6.
Please give Kudos if you like the explanation.
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Please give Kudos if you like the explanation.
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21 Aug 2019, 08:14
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vijyband99
I'm still confused. I don't follow the bold part if your explanation..
