Because breaking out your calculator when you want to figure out whether you can divide 22 students evenly into groups of three is going to get you laughed at.

Because breaking out your calculator when you want to figure out whether you can divide 22 students evenly into groups of three is going to get you laughed at. Divisibility by 13 is of course not as useful/applicable as divisibility by three, but the question is then more nuanced: "Why should I memorize this particular divisibility trick?"