These "rules" help us determine whether or not certain numbers are factors of a target number. We have wondered how people came up with these rules, and interestingly enough, some numbers have more than one rule of divisibility that will work. There are tests to determine divisibility for 4, 7, 8, 11, etc. but some of them are quite complicated. In the fifth grade, we are learning the rules for 2, 3, 5, 6, 9, 10, 12, and 15.
Here are some links to help you practice the rules of divisibility. First, a video from Khan Academy to review the rules for recognizing divisibility. Then, visit this site, Math Is Fun!, to study the different "tests". Next, some websites to practice what you've learned. IXL Divisibility Rules and Vectorkids Divisibility Rules.
Can you figure out why these rules work? It's not magical, it's mathematics! Practice, learn, and have fun!