How many positive integers less than or equal to 100 have a prime factor that is greater than 4?

97, 89, 83, 73, 71, 67, 61, 59, 53, 47,94,43,86, 41, 82, 37,74, 31,62,93, 29,58,87, 23,46,69, 92, 19, 38,57,76,95, 17,34,51,68,85, 13,26,39,52,65,78,91, 11,22,33,44,55,66,77,88,99, 7,14,21,28,35,42,49,56,63,70,77,84,91,98,

5,10,15,20,25,30,40,45,50,60,75

Step-by-step explanation:

We have to find the  positive integers less than or equal to 100 have a prime factor that is greater than 4

First let us find out the prime factors greater than 4 and less than 100

They are

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Let us start from the highest.

Greatest is 97, next 89, 83, 73, 71, 67, 61, 59, 53, 47,94, 43,86, 41, 82, 37,74, 31,62,93, 29,58,87, 23,46,69, 92, 19, 38,57,76,95, 17,34,51,68,85, 13,26,39,52,65,78,91, 11,22,33,44,55,66,77,88,99, 7,14,21,28,35,42,49,56,63,70,77,84,91,98, 5,10,15,20100

i.e. we consider each prime number and write its multiples also below 100

Now let us remove the repititions.

The answer would be

97, 89, 83, 73, 71, 67, 61, 59, 53, 47,94,43,86, 41, 82, 37,74, 31,62,93, 29,58,87, 23,46,69, 92, 19, 38,57,76,95, 17,34,51,68,85, 13,26,39,52,65,78,91, 11,22,33,44,55,66,77,88,99, 7,14,21,28,35,42,49,56,63,70,77,84,91,98,

5,10,15,20,25,30,40,45,50,60,75