Factors and factor pairs

Hello, and welcome to Myriora Maths! How many ways can you arrange twenty-four counters into a neat rectangle? Each way shows us a pair of factors. Let's find them all!

Why do factors matter? Say you're setting out twenty-four chairs for a school play, in neat rows. You could have three rows of eight, or four rows of six. Factors tell you every way that works!

A factor divides a number exactly, with nothing left over. Twenty-four counters can make one row of twenty-four. Two rows of twelve. Three rows of eight. And four rows of six.

Factors come in pairs that multiply to make the number. One and twenty-four. Two and twelve. Three and eight. Four and six. What about five? Twenty-four divided by five leaves a remainder, so five isn't a factor. And after four and six, the pairs just flip around, so we can stop.

So the factors of twenty-four are: one, two, three, four, six, eight, twelve, and twenty-four. Eight factors!

Let's try one together. What are the factor pairs of twelve? Start at one, and work up. Say them out loud!

One and twelve. Two and six. Three and four. Four and three is the same pair flipped, so we stop. Twelve has six factors. Well done if you found them all!

Here's a question that catches lots of people. What are all the factors of twenty-four? Some people start at two, and forget one and twenty-four. But one times twenty-four is twenty-four, so they're factors too!

Your turn! How many factors does thirty-six have? Find the factor pairs first, then pick the right card. You've got fifteen seconds, or pause the video. Go!

Time's up! One and thirty-six, two and eighteen, three and twelve, four and nine, and six and six. Six and six is just one factor, so thirty-six has nine factors!

Quick review. A factor divides a number exactly. Factors come in pairs that multiply to make the number. Work up from one, and stop when the pairs meet. See you next time!