Twelve chairs

About this video

A teacher has twelve chairs and wants them in equal rows, with no chair left over and no gap. How many ways are there? This short animation tries them. Twelve in one long row is 1 × 12. Rows of six make 2 × 6, and rows of four make 3 × 4. Rows of five don't work: two rows of five use ten chairs and two are left over.

The numbers that make a rectangle of twelve are called its factors: 1, 2, 3, 4, 6 and 12. A factor of 12 is a number you can multiply by another number to get 12, and each rectangle shows two factors at once, so factors come in pairs: 1 and 12, 2 and 6, 3 and 4. Some numbers have many factors and some have very few. Seven chairs make only one long line, because rows of two or three always leave one chair over. Numbers like seven are special, and a whole module of the course is about them. This video goes with the Factors: Making Rectangles lesson of Number Theory Level 1 on Knaph.

Transcript

1. 0:00Twelve chairs. How many ways to make equal rows?
2. 0:04One row of twelve. Two rows of six. Three rows of four.
3. 0:12Rows of five? Two are left over.
4. 0:16So the factors of twelve come in pairs.
5. 0:21Seven chairs make only one long line.
6. 0:27Factors are the row lengths that make a rectangle.