Multiples and Factors

1. Multiples and Factors

2. Multiples • A multiple is a number that is in the times tables. • Multiples of 6 are 6, 12, 18, 24, 30… • Multiples of 20 are 20, 40, 60, 80, 100…

3. What are the multiples of… 4 • 4, 8, 12, 16, 20… 9 • 9, 18, 27, 36, 45… 30 • 30, 60, 90, 120, 150…

4. Factors • A factor is a number that divides exactly into another number. • Factors of 6 are 1, 2, 3 and 6 • Factors of 20 are 1, 2, 4, 5, 10 and 20

5. What are the factors of… 15 • 1, 3, 5, 15 28 • 1, 2, 4, 7, 14, 28 50 • 1, 2, 5, 10, 20, 25, 50

6. Start with any number: Write down all its factors: Add all but the largest: Write down the factors of the new number: Add all but the largest: … and so on … 9 1, 3, 9 1+3 =4 1, 2, 4 1+2 =3 1, 3 =1 Factor exploration

7. 9  4  3  1 This is called the factor chain for 9. Draw factor chains for these numbers: (a) 16 (b) 29 (c) 12 (d) 6 (e) a number of your choice (f) Challenge: 102 (this is long!)

8. Play “Juniper Green” • A game for 2 players, played on a grid like this:

9. Play “Juniper Green” • The first player puts a counter on an even number. • After that, players take turns, putting a counter on either a factor or a multiple of the last number covered. • The first player who is unable to cover a number loses.

10. Play “Juniper Green” • Show that this is a first player game by finding the winning strategy for the first player. • Try playing on different sized grids. Juniper Green is named after the school where it was invented. Thanks!

11. JRElse 2004