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Length of integer

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Length of integer

by joyseychow » Tue Jun 09, 2009 6:46 am
For any positive integer n, the length of n is defined as the 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?

(a) None
(b) One
(c) Two
(d) Three
(e) Four
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by yogami » Tue Jun 09, 2009 7:03 am
IMO in order for a 2 digit number to have six prime factors we should consider a combination of least prime factors to yield two digit numbers
They are:
2^6 = 64
or 3*2^5 = 96
Any other combination of prime factors will yield higher digit numbers
So I think the answer is
(c)
Whats OA?
200 or 800. It don't matter no more.
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by joyseychow » Sat Jun 13, 2009 12:31 am
yogami wrote:IMO in order for a 2 digit number to have six prime factors we should consider a combination of least prime factors to yield two digit numbers
They are:
2^6 = 64
or 3*2^5 = 96
Any other combination of prime factors will yield higher digit numbers
So I think the answer is
(c)
Whats OA?
OA is C. Basically, I've got to try from the lowest prime and work my way up.
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