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# Prof, In the same way, what is the power of 2 in 100!

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Prof, In the same way, what is the power of 2 in 100! [#permalink]

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27 May 2006, 06:47
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Prof, In the same way, what is the power of 2 in 100!

Thanks...
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27 May 2006, 11:16
amansingla4 wrote:
Prof, In the same way, what is the power of 2 in 100!

Thanks...

Considering 100! = 100x99x98x...1,
There are 50 even numbers. Hence power is 50 ......A
Multiple of 4 give us one extra 2 each time. Hence 25....B.
Multiple of 8 give us one extra 2 each time. Hence 12....D.
Multiple of 16 give us one extra 2 each time. Hence 6....E.
Multiple of 32 give us one extra 2 each time. Hence 3....F.
Multiple of 64 give us one extra 2 each time. Hence 1....G.
Thus total = 97.
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27 May 2006, 12:22
kapslock wrote:
amansingla4 wrote:
Prof, In the same way, what is the power of 2 in 100!

Thanks...

Considering 100! = 100x99x98x...1,
There are 50 even numbers. Hence power is 50 ......A
Multiple of 4 give us one extra 2 each time. Hence 25....B.
Multiple of 8 give us one extra 2 each time. Hence 12....D.
Multiple of 16 give us one extra 2 each time. Hence 6....E.
Multiple of 32 give us one extra 2 each time. Hence 3....F.
Multiple of 64 give us one extra 2 each time. Hence 1....G.
Thus total = 97.

absolutly.

first divide 100/2 = 50
second, 100/4 = 25
third, 100/8 = 12
forth 100/16 = 6
firth 100/32 = 3
sixth, 100/64 = 1
get the total = 50+25+12+6+3+1 =97

thats it...........
Re: Power of 2   [#permalink] 27 May 2006, 12:22
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