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
What is the greatest integer k for which 2^k is a factor of
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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
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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30! = 30*29*----*1bhumika.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
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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