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For any integer P greater than 1, P! denotes the product of all the in
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Updated on: 21 Nov 2019, 02:23
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Question Stats:
33% (01:46) correct 67% (01:43) wrong based on 86 sessions
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For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45^m is a factor of 48!?
Re: For any integer P greater than 1, P! denotes the product of all the in
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08 Nov 2019, 05:32
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IMO it should be \(45^m\)
\(45=3^2*5\)
highest power of \(3^2\) that can divide 48! is \([\frac{1}{2}\) \([\frac{45}{3}]+[\frac{45}{3^2}]+[\frac{45}{3^3}]]\)= 10
highest power of 5 that can divide 48! is \([\frac{45}{5}]+[\frac{45}{5^2}]\)= 9+1=10
Greatest integral value that m can have= min(10, 10)= 10
Kinshook wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45m is a factor of 48!?
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08 Nov 2019, 12:46
Kinshook wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45m is a factor of 48!?
Why cannot it be 11 \(\frac{48!}{45*11}=\frac{1*2*3*..5*...9*..11..*22...48}{1*3*3*5*11}\) = Integer This shows that 48! is divisible by 45*11, hence m can be 11 Am I missing anything ?
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Re: For any integer P greater than 1, P! denotes the product of all the in
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21 Nov 2019, 02:24
stne wrote:
Kinshook wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45m is a factor of 48!?
Why cannot it be 11 \(\frac{48!}{45*11}=\frac{1*2*3*..5*...9*..11..*22...48}{1*3*3*5*11}\) = Integer This shows that 48! is divisible by 45*11, hence m can be 11 Am I missing anything ?
There was a typo: 45m instead of 45^m. Edited.
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Re: For any integer P greater than 1, P! denotes the product of all the in
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21 Nov 2019, 02:37
Ans: 10; D 45=3^2+5^1 48/3+48/9+48/27= 16+5+1= 22; 3^2 occurs 11 times. 48/5+48/25=9+1= 10. 5 occurs once. Limit is set by 5 and ans is 10. Kudos if helped. Want to unlock gmatclub tests
Kinshook wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45^m is a factor of 48!?
Re: For any integer P greater than 1, P! denotes the product of all the in
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21 Nov 2019, 03:11
Bunuel wrote:
stne wrote:
Kinshook wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45m is a factor of 48!?
Why cannot it be 11 \(\frac{48!}{45*11}=\frac{1*2*3*..5*...9*..11..*22...48}{1*3*3*5*11}\) = Integer This shows that 48! is divisible by 45*11, hence m can be 11 Am I missing anything ?
There was a typo: 45m instead of 45^m. Edited.
Thank you Sir, was wondering about the same. Wonder why Kinshook did not look into this.
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Concentration: General Management, International Business
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Re: For any integer P greater than 1, P! denotes the product of all the in
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21 Nov 2019, 03:24
Kinshook wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45^m is a factor of 48!?
A. 1 B. 2 C. 5 D. 10 E. 11
45^m = (3^2 x 5)^m Highest power of 3 by which 48! can be divided is 16+5+1 = 22 Highest power of 9 by which 48! can be divided is 11
Highest power of 5 by which 48! can be divided is 9+1 = 10
Hence, greatest value of m can be 10 D is correct.
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33% (01:46) correct 
