let the length of a positive integer n represent the number of prime factors of n counting repetitions.length?

Question

of 36 is 4 as 36=2*2*3*3length of 64 is 6 = 2^6 the number of numbers less than 100 with maxium length is

a)5
b)4
c)3
d)2

Answer 1

d)2.

No number less than 100 can have length >= 7, because 2^7=128.

2^6=64, and if you change one of these 2's to a 3, you get 2^5*3=96. Increasing the value of any other factor will give you a number greater than 100.