Date Multiplying Challenge
Excel, 48 bytes

Hooray! Finally something Excel is actually good at. 

=COUNT(VALUE(ROW(1:12)&amp;"/"&amp;A1/ROW(1:12)&amp;"/"&amp;A1))


Takes input from A1 in the form of an integer 1-99 representing the year, and outputs to wherever you enter this formula. It's an array formula, so use Ctrl-Shift-Enter instead of Enter to enter it. 

This takes advantage of the fact that COUNT ignores errors, so any errors that are caused by either the month not dividing the year (leading Excel to parse something like 2/12.5/25 or by the date not being valid, like 2/29/58, are just silently ignored.