What Is a Factor Rainbow in Math?

A factor rainbow is a way of writing factors for numbers using a series of arcs. It helps students ensure they have all the factors by listing them in consecutive order.

A number’s factors are the pairs of smaller numbers that can be multiplied to make the larger number. When factoring 28, the problem solver begins with one and 28 then moves up to two and 14 and four and seven.

To write this in a factor rainbow, a one is written on the left side and a 28 on the right with an arc drawn between them. A two is then written to the right of the one with 14 written to the left of 28. An arc in a different color should join these two digits. Finally, four and seven are written inside the other factors, joined by a different-colored arc. The finished product is a rainbow, displaying the factors for 28.