Finding the prime factorizations of the numbers in the range $[1,10^8]$

Question

I want to find out prime factorization of all numbers between $[1,10^8]$ in $O(\sqrt{N})$.

I read a lot of material on divisors and prime factorization and finally found that if I have Sieve of Eratosthenes having primes upto $10^4$,I can find out prime factorization of numbers between $[1,10^8]$ ? But How do I do that ?