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What is the greatest integer k for which 2^k is a factor of

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by bhumika.k.shah » Mon Jan 25, 2010 8:30 pm
What is the greatest integer k for which 2^k is a factor of 30!

A.22
B.25
C.28
D.26
E.32

OA D

I dont know how to approach these kinda sums..if someone could help me how to deal with such kinda sums that would be of great help!

Thanks :D
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by thephoenix » Mon Jan 25, 2010 8:49 pm
imo D

30/2=15----->15
15/2=7.5------->7
7/2=3.5------>3
3/2=1.5---->1

add 15+7+3+1=26

hence k is 26

another method

there are 15 no div by 2------------>15
4,8,12,16,20,24,28 all these no carries one extra(2*2;4*2;6*2;10*2;12*2;14*2) 2--------->7
8,16,24 one extra(2*2*2;8*2;2*6*2) 2-------->3
16 one more (2*2*2*2)2------->1

tot 26
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by ajith » Tue Jan 26, 2010 1:16 am
bhumika.k.shah wrote:What is the greatest integer k for which 2^k is a factor of 30!

A.22
B.25
C.28
D.26
E.32

OA D

I dont know how to approach these kinda sums..if someone could help me how to deal with such kinda sums that would be of great help!

Thanks :D
30! = 30*29*----*1

There are 15 even numbers, which will give a factor of 2^15
there are 7 multiples of 4 which will additionally give 2^7
there are 3 multiples of 8 which will additionally guve 2^3
there is a multiple of 16 which will give another 2

k = 15+7+3+1 = 26
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