A Hamming number is a positive number which has no prime factor larger than 5.
So the first few Hamming numbers are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15.
There are 1105 Hamming numbers not exceeding 108.
We will call a positive number a generalised Hamming number of type n, if it has no prime factor larger than n.
Hence the Hamming numbers are the generalised Hamming numbers of type 5.
How many generalised Hamming numbers of type 100 are there which don’t exceed 10^9?
Hint: Generate prime number less than 100. Check for all the number in range 1-10^9, whether all prime number <100 divides them totally to get final remaining number as 1. Is this happens for particular number then add it to your list otherwise don’t add the number to the list.