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duttsit
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 18:22
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If 2^k is a factor of 20!, what is the maximum value of integer k?



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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 18:58
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20!=1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20
2's in:
2=1
4=2
6=1
8=3
10=1
12=2
14=1
16=4
18=1
20=2
total = 18

therefore, k= 18
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 19:42
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Titleist

18 I used the same method as Himalaya.
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Me too. 2 + 1 makes 3 :-D
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 19:48
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18 for me too...

here is how I would do this...

20/2=10 times you will see 2...

now there are some instances where you have more 2s...like 4

20/4=5 so you have 5 more 2s...

now look at 8, you get 1 more 2 from 8, 2 more from 16...

so total number of 2s you see are 10+5+1+2=18
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 20:04
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Good job guys. OA is 18. Fresinha method might save some seconds.

PS: Titleist I see myself promoted to VP as well :) do I get some soup?
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 20:10
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duttsit
Good job guys. OA is 18. Fresinha method might save some seconds.

PS: Titleist I see myself promoted to VP as well :) do I get some soup?
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NO SOUP FOR YOU!!!
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 20:12
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fresinha12
18 for me too...
here is how I would do this...
20/2=10 times you will see 2...
now there are some instances where you have more 2s...like 4
20/4=5 so you have 5 more 2s...
now look at 8, you get 1 more 2 from 8, 2 more from 16...
so total number of 2s you see are 10+5+1+2=18
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i could not eat it..................
freshina explain your newtonian mathmatics.... :wink:
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 20:14
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Okay Okay Duttsit I have special soup for you!
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 20:17
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Titleist
Okay Okay Duttsit I have special soup for you!
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Yahoo!! First one to get soup from Titleist. BTW, I liked this Underpants Gnomes story :) You can see it in action everywhere around work :)
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 20:39
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duttsit
Titleist
Okay Okay Duttsit I have special soup for you!

Yahoo!! First one to get soup from Titleist. BTW, I liked this Underpants Gnomes story :) You can see it in action everywhere around work :)
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Which story are you refering to? The parody of businesses with bad or no business models (i.e. dotcoms) or the rampant stealing of underpants by these crazy gnomes? You see underpants gnomes stealing underpants from your unsuspecting colleagues at your office? :P
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If 2^k is a factor of 20!, what is the maximum value of 03 Nov 2005, 21:55
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Ok the whole idea is to find the number of times 2 appears in 20!

2*3*4*5*6....*20

so you can see the that 2 appears once in 2, twice in 4, once in 6, three times in 8....etc....

so bascially divide 20/2= this give you the times you will see a single factor of 2...but there are instances like 4, where you have 2 appear two times, ei.e 2*2 but we only counted 2 once...so you need to account for these additional twos..so 20/4=5 these are the additional 2s we get from 4 which appears in 20!...now 8 which has 3 twos in it also appears in 20! once as 8 and the second time as 8*2=16=2.2.2.2, but remember we have already counted one 2, when we divided 20/2, we accounted for the other factors of 2 which comes with 4...and now we have to account for the set of 2s that appear with 8 which is one more 2..that we didnt count..
so total number of times we see 2 in 20! is 18 times...

just like you did...just here its more efficient to look at it this way...
HIMALAYA
fresinha12
18 for me too...
here is how I would do this...
20/2=10 times you will see 2...
now there are some instances where you have more 2s...like 4
20/4=5 so you have 5 more 2s...
now look at 8, you get 1 more 2 from 8, 2 more from 16...
so total number of 2s you see are 10+5+1+2=18
i could not eat it..................
freshina explain your newtonian mathmatics.... :wink:
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