1. Prime Factors/ Indices

2. Objectives By the end of the lesson learners will be able to: Identify Prime Factors (Process of the Factor Tree) Express a number as a product of its prime factors. Identify the LCM and LCF using Venn diagrams. Use powers (also known as indices)

3. Prime Factors We can use a ‘factor tree’ to enable us to write a number as “a product of its prime factors” Each time you reach a prime number, you stop and circle that number

4. Example: Write 84 as a product of its prime factors 84 = 2 x 2 x 3 x 7 84 = 2 2 x 3 x 7 84 242 221 37

5. Prime Factors Write 420 as a product of prime factors.

6. Your turn… 1.Find the HCF of the following: a)18 and 28 b)16 and 40 c)42 and 90 d)40 and 63 e)20, 64 and 108 f)54, 90 and 162 2.Find the LCM of the following: a)4 and 5 b)8 and 12 c)6 and 9 d)12 and 15 e)5, 8 and 10 f)4, 7 and 9 3.Write the following as products of their prime factors. a) 18b) 135c) 154d) 2310 2 8 6 1 4 18 20 24 18 60 40 252 3 2 x 2 3 3 x 5 2 x 7 x 11 2 x 3 x 5 x 7 x 11

7. HCF and LCM Calculate the HCF and LCM of 48 and 60 4860 48 = 2 x 2 x 2 x 2 x 3

8. 60 = 2 x 2 x 3 x 5 48 60 2 2 2 2 3 3 22 5 Multiply the numbers in the overlap to get the HCF Multiply all the numbers in the Venn diagram to get the LCM. HCF = 2 x 2 x 3 = 12 LCM = 2 x 2 x 3 x 2 x 2 x 5 = 240 Find the HCF and LCM of the following: 24 and 30 36 and 50 16 and 72

9. 3535 5858

10. Introduction What does 4 2 actually mean? 4×4 16

11. Introduction What does 4 5 actually mean? 4×4×4×4×4

12. Introduction How can we write 5×5×5×5 5454 This is 5×5×5×5 written in INDEX FORM

13. Writing in Index Form Write the following in Index Form 8×8×8×8 = 3×3×3×3×3×3 = 9×9×9= 8484 3636 9393

14. Indices 3 x 3 x 3 x 3 3 x 3 x 3 3 x 3 3 = 3 4 = 3 3 = 3 2 = 3 1

15. Multiplying Indices Simplify the following leaving in index form. 8 3 × 8 4 = 8×8×8×8×8×8×8 = 8 7 Is there a quick way you can work this out? 8 3 × 8 4 = 4 8 = 8 7 + 3 8484 83 83 Remember this only works for numbers with the Same base number

16. Multiplying Indices Simplify the following leaving in index form. 5 2 × 5 4 = 5×5×5×5×5×5 = 5 6 The Quick Way!!! 5 2 × 5 4 = 4 5 = 5 6 + 2 5454 52 52 Remember this only works for numbers with the Same base number

17. Dividing Indices Simplify the following leaving in index form. 1. 2 5 ÷ 2 2 = = 2 3 The Quick Way!!! 2 2525 25252 = 2x2x2x2x2 2x2 1. 2 5 ÷ 2 2 = 2 2 = 2 3 - 5 Remember this only works for numbers with the Same base number

18. Indices Simplify the following leaving in index form. 1.(( 2 3 ) For these it is best to write them out! 2 2 3 x 2 3 This means this = 2 6 Remember this only works for numbers with the Same base number

19. Indices Simplify the following leaving in index form. 1.(( 3 5 ) For these it is best to write them out! 3 3 5 x 3 5 x 3 5 This means this = 3 15 Remember this only works for numbers with the Same base number

20. Questions Simplify the following numbers, leaving your answers in index form: 1.(a)2 3 x 2 2 (b)3 5 x 3 2 (c)7 3 x 7(d)9 5 x 9 2 2.(a)2 3 ÷ 2 2 (b)3 5 ÷ 3 2 (c)7 3 ÷ 7(d)9 5 ÷ 9 2 2525 3737 7474 9797 23 7272 9393

21. Indices with Letters a x a x a x a a x a x a a x a a = a 4 = a 3 = a 2 = a 1

22. Multiplying Indices Simplify the following leaving in index form. a 3 × a 4 = a × a × a × a × a × a × a = a 7 Is there a quick way you can work this out? a 3 × a 4 = 4 a = a 7 + 3 a4a4 a3 a3 Remember this only works for numbers with the Same base number

23. Indices with Letters 3a 5 x2a 2 = x =3x2x =6a 7 3 a 5 2 a2a2 a x a x a x 3 x a x a x a x a x a2 x a x a x a x a a x a

24. Indices with Letters 6a 3 x3a 2 =6xaxaxax =6x3x =18a 5 3xaxa6a3a3 3a2a2 axaxaxa x a 6a 3 x3a 2 6a3a3 3a2a2 The Quick Way!!! = xx 2 3 a + = 18a 5

25. Questions Simplify the following numbers, leaving your answers in index form: 2.(a)(2 3 ) 2 (b)(3 5 ) 2 (c)(7 3 ) 3 (d)(9 2 ) 5 2626 3 10 7979 9 10 3.(a)3b 3 x 7b 5 (b)(c)(d)5b x 2b 7 2b 3 x 6b 3 2b 3 x 15b 2 21b 8 10b 8 12b 6 30b 5 1.(a)a 3 x a 2 (b)a 5 x a 6 (c)a x a 3 (d)a 2 x a 12 a5a5 a 11 a4a4 a 14