b) Use (part a) above to find the prime factorization of 20!
The prime numbers < 20 are 2,3,5,7,11,13,17,19
So apply the formula for all of these, so that you get their highest power in 20! And this gives the prime factorisation of 20!
c) one zero at the end = 1 factor 10. 10=2x5. So see what's the power of 5 in the prime factorisation of 100! also find the power of 2, though the latter is not useful since one can see that there are much more factors 2 than 5.