Divisibility Rules

I often run into students who need to do a complex operation in algebra or even up through calculus, but they struggle because they are missing a skill from a much simpler time. One of the skills that I see students are missing is being able to quickly determine if a number is divisible by a digit between 2 and 9 in order to simplify and reduce fractions, roots, factor equations, and more. One way to fix this is through practice and learning a few tricks. Even when students are in upper level classes. It’s never too late!

To make this easier for students to learn, it helps to have a list to use, like training wheels while they work to memorize how to find possible factors. To that end, I’ve made a great printable in both color and black and white which explains each rule, then gives two examples and a counterexample so students can see at a glance how to check for divisibility. If you print it two pages per sheet, you can have all of them on one side or print them front and back so you have them just a bit bigger!

How can you use this printable to learn the rules? Well, firstly you can use the chart while doing math work. But sometimes you want a fun way to practice the skill first before you need it. To that end, try these ideas:

  • Get 3-5 (or more!) dice and roll them. Line the dice up to make a number and figure out if that number is divisible by anything between 2 and 9. For example, roll 3 dice and get a 2, a 5, and a 3. Use the number 253 (or 235 or 352 and so on) and figure out if it’s divisible using the chart. If they are successful, they get that number of points (2+5+3=8, so 8 points)
  • Using similar rules, take a deck of cards out and make numbers by picking cards at random and lining them up. This works best if you take out the aces and face cards, but leave 10. If you put 10 into a number, you can fit zeros in that you don’t normally get with dice. For example, you pick a 5, an 8, a 10, and a 3, so you have the number 58,103 to test divisibility rules on.
  • For some competition, you can have kids race against each other. If that causes too much friction, do several rounds and have the kids try to beat their own previous best scores. This can be a great 5-10 minute warm-up or break time to make the day more interesting and get the body and brain moving.
  • Math War: Each student gets half of the deck of cards. Using their own stack face-down, they flip over 3 cards to create a 3+ digit number using the rules above. In this case, assign face cards a value of 10 and aces a value of 1. Use the divisibility rules to find the largest number between 2 and 9 that is a factor of the number formed by the cards. Whoever has the largest number gets to keep all the cards and everyone lays out 3 more cards until one person has all the cards.

This skill is really useful from middle school on up. I can’t emphasize this enough. Whether students are trying to find a common denominator, write a prime factorization, or just doing mental math in general, being able to quickly determine if a large number can be broken down more easily is a huge skill for students to master. If a student is still struggling with a basic skill, learning advanced material will be that much harder.

This skill is learned in chapter 4 of my pre-algebra class, but you can get this great free resource today just for signing up for my email list below! Please share this post if you know anyone who might want the file for themselves!

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