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For any positive integer n , n > 1, the

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VP
Joined: 22 Oct 2006
Posts: 1438
Schools: Chicago Booth '11
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Kudos [?]: 192 [0], given: 12

For any positive integer n , n > 1, the [#permalink]

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08 Mar 2007, 21:09
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For any positive integer n , n > 1, the "length" of n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)

What is the greatest possible length of a positive integer less than 1000?

A)10
B)9
C)8
D)7
E)6
Senior Manager
Joined: 29 Jan 2007
Posts: 442
Location: Earth
Followers: 2

Kudos [?]: 63 [0], given: 0

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08 Mar 2007, 23:37
I go with B = 9.

Reasoning is...

for max length take smallest prime allowed (2) and keep multiplying till you reach 1000

2*2*2*2*2*2*2*2*2 = 2^9 = 512
2^10 = 1024

So max length is 9

(This is the first question I could answer before anyone else...small joys)
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Joined: 03 Mar 2007
Posts: 14
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Kudos [?]: 0 [0], given: 0

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09 Mar 2007, 03:52
I agree with kyatin's solution. I would request terp26 to also share with us the problems/doubts/issues faced when actually solving this problem. And also if kyatin's solution was helpful.
09 Mar 2007, 03:52
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