Divisibility Tests are useful so one can tell if a number is a factor of a given number without dividing.
Divisibility Tests for 2, 3, 5, 7 and 11:
http://www.youtube.com/watch?v=rm9kPMf1cEY
Divisibility Tests for 11 and 13:
http://www.youtube.com/watch?v=X7MgbK_S9O0