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# PS : prime factors

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Senior Manager
Joined: 16 Jan 2009
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Concentration: Technology, Marketing
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PS : prime factors [#permalink]  03 Jun 2009, 13:26
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For any positive integer n, the length of n is defined as number of prime factors whose product is n, For example, the length of 75 is 3, since 75=3*5*5. How many two-digit positive integers have length 6?
0, 1, 2, 3, 4

[spoiler]The least prime number is 2. We notice that 2^6=64 and 2^5*3=96. Any 2 combined, the number will be greater than 100. So, only 64 and 96 fulfill the requirement.
IMO 2.[/spoiler]
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Lahoosaher

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Re: PS : prime factors [#permalink]  03 Jun 2009, 14:20
2*2*2*2*2*2 = 64
2*2*2*2*2*3 = 96
Senior Manager
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Re: PS : prime factors [#permalink]  04 Jun 2009, 01:04

2*2*2*2*2*2 = 64..

now replace one of the 2 with 3..

2*2*2*2*2*3 = 96..

now replace one more 2 with 3..

2*2*2*2*3*3 = 154 doesnt satisfy..

hence hte answer will be 2..
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Re: PS : prime factors [#permalink]  04 Jun 2009, 03:34
2^6 = 64
3^6 will be a 3 digit number

2^5 * 3 = 96

So 64, 96; Answer is 2
Re: PS : prime factors   [#permalink] 04 Jun 2009, 03:34
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