Ws1 Factors Multiples

Date:

______/______/ 2009

Marks

Worksheet 1: Factors and Multiples (Prime Factorisation) 1

Basic Question (a) Express 5 832 as a product of prime factors. (b) Hence, find the value of 3 5 832 . Solution: (a) 5832 = 23 × 36 (b) 3 5 832 = 3 23 × 36 2 3

=

3

(2×3 )

=

3

(18)

3

= 18

[Cedar Girl’s Sec School/2008] Ans: (a) 23 × 36 (b) 18

2

Intermediate Question (a) Express 5445 as a product of prime factors. (b) Hence, find the smallest integer, k such that 5445k is a perfect cube. Solution: (a)

5445 = 32 × 5 ×112

(b)

5445k = 3 2 ×5 × 112 × k ∴k

= 3 × 52 × 11 = 825

[Crescent Girl’s School/2008] Ans: (a) 32 × 5 × 112 (b) 825

© Victoria School Math Department

3

Intermediate Question Find the smallest positive integer which can be multiplied by 540 to give a cube number. Solution:

540 = 22 × 33 × 5 ∴ smallest number to get a cube number = 2 × 52 = 50 [Cedar Girl’s Sec School /2008] Ans: 50

4

Intermediate Question (a) Express 294 and 390 as products of prime factors using index notation. (b) Write down the smallest value of n for which 294n is a square number. Solution:

(a) 294 = 2 × 3 × 7 2 390 = 2 × 3 × 5 × 13 (b) 294n = 2 × 3 × 7 2 × n ∴n = 2×3 =6 [Cedar Girl’s Sec School/2007] Ans: (a) 294 = 2 × 3 × 7 2 , 390 = 2 × 3 × 5 × 13 (b) 6

5

Advance Question (a) Express 7225 and 9261 as products of prime numbers in index notation. (b) Hence, evaluate

7225 − 3 9261

Solution:

(a)7225 = 52 ×17 2 9261 = 33 × 73

7225 − 3 9261

(b) = =

( 5 ×17 )

2

− 3 (3× 7)

3

( 5 ×17 ) − ( 3 × 7 )

= 85 − 21 = 64 =8

Ans:(a) 7225 = 52 × 17 2 ,9261 = 33 × 73 (b) 8

© Victoria School Math Department