jmc

The easiest solution is to find the number of positive integers with only 2 and 3 as their prime factors. If the number has no factors of 3, the qualifying numbers are $2^0,2^1,2^2,2^3,2^4,2^5,2^6$ for 7 total. If there is one factor of 3, we have $2^0\cdot 3^1,2^1\cdot 3^1,2^2\cdot 3^1,2^3\cdot 3^1,2^4\cdot 3^1,2^5\cdot 3^1$ for 6 total. With two factors of 3, we have $2^0\cdot 3^2,2^1\cdot 3^2,2^2\cdot 3^2,2^3\cdot 3^2$ for 4 total. With three factors of 3, we have $2^0\cdot 3^3,2^1\cdot 3^3$ for 2 total. Finally, $3^4$ gives us 1 more. So, there are $7+6+4+2+1=20$ positive integers less than or equal to 100 that have only 2 and 3 as prime factors. Therefore, there are $100-20=\boxed{80}$ positive integers less than or equal to 100 that have a prime factor greater than 4.