# Factors vs. Multiples

Have you ever wished that there was a magic word that you could say to get your students to understand and identify the difference between factors and multiples? You are not alone!

Factors and multiples are introduced in elementary school between 4th and 5th grades. It’s amazing to so many secondary math teachers that by the time a student reaches middle school many students continue to struggle with identifying a number as either a factor or a multiple.

Students encounter factors and multiples long before they are taught the distinct difference between a factor and a multiple.

Multiplication is taught conceptually at the end of 2nd grade two years before the term factor or multiple are “formally” introduced.  To help students with distinguishing between factors and multiples 2nd and 3rd grade teachers can introduce the term factor to their students when they begin teaching multiplication. When I teach multi-digit multiplication I refer to numbers as factors so that my students know that factors are single digit and multi-digit numbers that are multiplied together. So when I actually begin to teach factors or factorization my students will have heard the term factor more than once.

I also use a Frayer model to help cement the students’ understanding of what a factor is and what it is not. I also give the students a list of numbers to classify as either factors or multiples and then use a Venn diagram to classify the list of numbers as factors or multiples.

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