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?  Select
A) 0
B) 1
C) 2
D) 3
E) 4
Length of a number = Total number of prime factors of the number.   Any composite number can be represented as a product of prime numbers as shown below:   N= 2^x * 3^y * 5^z * 7^a ...so on   Since our requirement is a two digit number, we shall raise maximum power for smallest prime factor.   N= 2^6 = 64 has Length 6   N= 2^5 * 3 = 96 has length 6   N=2^4 * 3^2 = 144 is a three digit number and so on the other combinations would reveal 3 digit numbers.   Hence there are only 2 numbers   ANSWER:2
<result>C</result>
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?