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Length of numbers -C

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by tanyajoseph » Sat Sep 01, 2007 10:44 am
FOr any positive integer n, the length of n is defined as the no of prime factors whose product is n. FOr eg., the length of 75 is 3, since 75 = 3*5*5.
How many two digit integers have length 6?

A) None
B) One
C) Two
D) Three
E) FOur
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by keepsmilinyaar » Sat Sep 01, 2007 11:13 am
As the length is 6, we need to consider all the numbers less than 100.

2 is the least prime number so we can start with 2.

Number 1: 2^6 = 64
Number 2: (2^5) * 3 = 96

If we go any further by trying to reduce the power of 2, we will get a number > 100. Therfore if this is the case with 2, then defintitely the prime numbers > 2 will give one numbers > 100.

So is the answer 2. ie C
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by agps » Sat Sep 01, 2007 11:19 am
"As the length is 6, we need to consider all the numbers less than 100. "

why? I'm missing something here. :(
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by keepsmilinyaar » Sat Sep 01, 2007 11:23 am
I'm sorry about the statement there. Am not too good at putting down mental thoughts.

What i meant was..

As the length is 6, and we need to consider all the two digit numbers i.e. numbers less than 100
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by agps » Sat Sep 01, 2007 11:33 am
"How many two digit integers have length 6? "

Damn :evil: , missed that part, thanks keepsmilinyaar
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