In order for knowledge of basic multiplication facts to be fully ingrained, the ability to look at a number and quickly determine its factors is crucial. The Finding Factors cards in my store are an introduction to that.
Once factors are understood well, the DIVISIBILITY fun begins! To teach the Rules of Divisibility, students highlight the multiples of a number on a 1-100 chart, and see if they can figure out a rule for numbers that are divisible by that factor. First, the easy ones: 10, 5, and 2. Most kids can figure these out easily. Then, 3, 9 and 6, which they will likely need some help with (though there is a clue on that page), but the summing of digits is not hard once learned. Finally, 4 and 8. There is a rule for finding whether a number is divisible by 7, but it’s REALLY complicated and not particularly helpful (nor, to my mind, worth the trouble).
With the following charts, you can help your student(s) discover the rules of divisibility for 10, 5, 2, 3, 9 and 6. I usually introduce only these 6 rules, which is enough to give a boost in finding greatest common factors (GCF) for simplifying fractions.
To find whether a number is divisible by 4 or 8 involves finding whether the last two (in the case of 4) or the last three (in the case of 8) digits are divisible by 4 or 8. There are several ways to find out if a number is divisible by 7, none of which is at all practical. To my mind, the only reason to go beyond the first six is if students are really interested. In case they are, here’s a sheet that explains the rules for 4, 8 and 7.
Look for the "Finding Factors Cards - all numbers 0-144" as a way to test new-found knowledge of divisibility rules and learn how to prime factor, and "Divisibility - Learning and Games." (free!).