Calculating the prime factors from prime sieve. Why is the time complexity O(logn)?

#1

I have a problem in understanding that why is the time complexity of finding prime factors using prime sieve O(log n)? Can someone please explain.

#2

In the calculation step we are dividing the number every time by the smallest prime number till it becomes 1.
So, let’s consider a worst case in which every time the smallest prime factor is 2 . Therefore will have log n division steps.
Hence, We can say that our Time Complexity will be O(log n) in worst case.