Call a date \( mm/dd/yy \) \textit{multiplicative} if its month number times its day number is a two-digit integer equal to its year expressed as a two-digit year. For example, \( 01/21/21 \), \( 03/07/21 \), and \( 07/03/21 \) are multiplicative. Find the number of dates between January 1, 2022 and December 31, 2030 that are multiplicative.

Let's think step by step and output the final answer within \boxed{}.
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