A skill that 5th-grade kiddos have trouble with is finding factors. There’s a couple of reasons for that. First, if kids aren’t strong with their multiplication facts, finding factors is excruciating. Next, kids only tend to think of the facts they know. So, for instance, they don’t realize that 2 and 18 are factors of 36. Finally, they don’t use an organized process to find all the factors. They skip around, just trying to remember the facts they know, so they end up leaving some out. I teach my kiddos a very structured process for finding factors that seems to work.
First, we organize our work in a t-chart. Students write the number they are finding factors for at the top of the chart.
Next, we go through each single-digit number and decide if it’s a factor or not. It sounds something like this:
Is 1 a factor? Yes. 1 and what? 1 and 36.
Is 2 a factor? Yes. How do you know? Because it’s even. 2 and what? 2 and 18 (they divide if they don’t know).
Is 3 a factor? Yes. 3 and what? 3 and 12.
Is 4 a factor? Yes. 4 and what? 4 and 9.
Is 5 a factor? No. How do you know? Because 36 doesn’t have a 0 or 5 in the 1s place.
Is 6 a factor? Yes. 6 and what? 6 and 6.
Is 7 a factor? No. How do you know? 7 x 4 is 28 and 7 x 5 is 35.
Is 8 a factor? No. How do you know? 8 x 4 is 32 and 8 x 5 is 40.
Is 9 a factor? Yes, but we already have it on our list.
So then they are done! Notice that students are expected to use knowledge about even and odd numbers and the divisibility rules for 3 and 5.
To find common factors, students create two t-charts. After finding the factors for both numbers, they circle the factors that are on both lists.
Ready to try it with your kiddos? Use the link below to download a set of cards for a workstation that can be used for finding factors and common factors. To work only on factors, students just choose one card. To find common factors, students choose two. For an even greater challenge, have them choose three.