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exact power of 5

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by sanju09 » Tue Mar 16, 2010 4:50 am
What exact power of 5 divides 87! (read factorial 87)?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 23
The mind is everything. What you think you become. -Lord Buddha



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by kstv » Tue Mar 16, 2010 5:02 am
87! is 1 * 2 *....5......10.....25.......50........75......80 .....85*86*87
5¹ will divide each of 5 , 10 for 10 we need 2 so till 85 we need 17 so 5 to the power 17
but 5² is needed to divide 25,50, 75 all multiple of 25
i.e. another 5³
IMO D
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by harshavardhanc » Tue Mar 16, 2010 6:14 am
sanju09 wrote:What exact power of 5 divides 87! (read factorial 87)?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 23
a short cut :

the power will be :

Sum of quotients of division of 87 by powers of 5 ( you need to take all the powers which are less than or equal to 87) :

hence, in our case :

87/5+87/(5^2) ---------- you can't take third power of 5 because it is greater than 87.

therefore, answer = 17 + 3 = 20
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Harsha
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by sanju09 » Tue Mar 16, 2010 6:21 am
harshavardhanc wrote:
sanju09 wrote:What exact power of 5 divides 87! (read factorial 87)?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 23
a short cut :

the power will be :

Sum of quotients of division of 87 by powers of 5 ( you need to take all the powers which are less than or equal to 87) :

hence, in our case :

87/5+87/(5^2) ---------- you can't take third power of 5 because it is greater than 87.

therefore, answer = 17 + 3 = 20
That's perfect!
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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