In SQL Server, a clustered index organizes the data in a table based on the index key. The fill factor setting determines how much space on each page is left free for future growth, which affects how many rows fit on each page.

Here's how the fill factor affects the number of free rows per page:

Fill Factor: This percentage indicates how full each page should be when data is inserted. For example, a fill factor of 20% means that only 20% of each page will be used for data, leaving 80% of the page free for future growth. Conversely, a fill factor of 40% means that 60% of each page is free.

Calculating the Relationship:

Understanding Fill Factor and Free Space:
    Fill Factor = 20%: This means that 20% of each page is filled with data, leaving 80% of the page free.
    Fill Factor = 40%: This means that 40% of each page is filled with data, leaving 60% of the page free.

Number of Free Rows Per Page:

Let's assume the total number of rows that a page can hold when completely full is RR.
    For a fill factor of 20%, the free space is 80% of the page:
    Free Rows per Page=0.80×R
    Free Rows per Page=0.80×R
    For a fill factor of 40%, the free space is 60% of the page:
    Free Rows per Page=0.60×R
    Free Rows per Page=0.60×R

Relating Free Rows (A and B):

Let AA be the total number of free rows per page for the fill factor of 20%.
Let BB be the total number of free rows per page for the fill factor of 40%.

We can write:
A=0.80×R
A=0.80×R
B=0.60×R
B=0.60×R

To find the relationship between AA and BB:
AB=0.80×R0.60×R=0.800.60=43≈1.33
BA​=0.60×R0.80×R​=0.600.80​=34​≈1.33

Therefore:
A=1.33×B
A=1.33×B

Conclusion

The correct relationship between AA and BB is: A=1.33B A=1.33B

So, the number of free rows per page with a fill factor of 20% (A) is 1.33 times the number of free rows per page with a fill factor of 40% (B).