Finding Factors and Common Factors

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

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.

finding common factors

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.

finding common factors

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.

finding common factors
Click here to download your free cards!

12 Comments

  1. Haley D.

    This is exactly how I teach my 5th graders to find factors, only I haven’t used a t-chart. Thanks for the tip!

    Reply
    • Donna Boucher

      My pleasure, Haley!

      Reply
  2. Anonymous

    I teach it this way as well, but will try using the t-chart! I do tell my kids that when you get to a double (6×6), you can stop. Even though a higher number may be a factor, they will already have it on the list,(as the 9 in your example).

    Reply
    • Donna Boucher

      Oh, that’s a great tip! Thanks for sharing. 🙂

      Reply
  3. Amy Dahmke

    The T Chart is Great!!!! I taught first graders with Math Expressions as a guide and the T Chart made it so concrete for them! Love it 🙂

    Thanks for the number cards!!!!

    Amy @ 3amcreations.blogspot.com

    Reply
    • Donna Boucher

      So glad the t-chart worked for you, Amy. 🙂

      Reply
  4. Cindy Calenti

    Great tip – thank so much for sharing! I love your math instruction ideas they are so helpful and creative.

    Cindy
    Granny Goes to School

    Reply
    • Donna Boucher

      Always love seeing your comments, Cindy! Thanks so much! 🙂

      Reply
    • Lynn

      Just be careful not to stop too soon. There may be factors larger than a single digit. 121 has a factor of 11. I teach my kids to stop when there are no more factors in between their bottom left and right hand factors.

      Reply
  5. Cindy in Wisconsin

    Much appreciated! Thanks!

    Reply
    • Donna Boucher

      My pleasure, Cindy! 🙂

      Reply
  6. Anonymous

    I teach high school and have had to teach many remedial classes. This is ALWAYS how I have taught factors. It works itself into factoring binomials really well. THANK YOU for getting this out and into the younger grades. It really does work!

    Reply

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