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# What is the least number that should be multiplied to 100!

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Director
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What is the least number that should be multiplied to 100! [#permalink]

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11 Nov 2005, 22:11
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the least number that should be multiplied to 100! to make it perfectly divisible by 3^50?
(a) 144
(b) 72
(e) 108
(d) 216
(e) 789

is there any short cut for these type of question .....?
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11 Nov 2005, 22:46
cool_jonny009 wrote:
What is the least number that should be multiplied to 100! to make it perfectly divisible by 3^50?
(a) 144
(b) 72
(e) 108
(d) 216
(e) 789

is there any short cut for these type of question .....?

The largest power of 3 to be divisible by 100! is 3^48
so to make 100! perfectly divisible by 3^50 , we need to multiple 3^2 to 100! ...72 is the least number containing 3^2. thus 72
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11 Nov 2005, 22:58
Agree with Laxieqv.

Just to explain how she got 3^48 in 100!

100! has:
100/3 = 33 3's
100/9 = 11 9's
100/27 = 3 27's
100/82 = 1 81's

33 + 11 + 3 + 1 = 48
wonder why 3^2 = 9 is in AC.
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Director
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11 Nov 2005, 23:52
OA is B.....you guys are too good...
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12 Nov 2005, 03:41
yup got 3^2 = 9 as well

72 is closer to 9 than any other choice... so B it is.
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12 Nov 2005, 03:41
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