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Factors

Factors. Factors. Example : Find the factors of 56. Numbers that divide into 56 without leaving a remainder. F56 = 1 and 56. 2 and 28. 4 and 14. 7 and 8. Factors. Factors. Example : Find the factors of 64. Numbers that divide into 64 without leaving a remainder.

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Factors

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  1. Factors Factors Example : Find the factors of 56. Numbers that divide into 56 without leaving a remainder F56 = 1 and 56 2 and 28 4 and 14 7 and 8

  2. Factors Factors Example : Find the factors of 64. Numbers that divide into 64 without leaving a remainder F64 = 1 and 64 2 and 32 4 and 16 8 and 8

  3. Factors Factors Example : Find the factors of 24. Numbers that divide into 24 without leaving a remainder F24 = 1 and 24 2 and 12 3 and 18 4 and 6

  4. Factors Highest Common Factor Highest Common Factor Largest Same Number We need to write out all factor pairs in order to find the Highest Common Factor.

  5. Factors Highest Common Factor Example : Find the HCF of 8 and 12. F8 = 1 and 8 2 and 4 F12 = 1 and 12 2 and 6 3 and 4 HCF = 4

  6. Factors Highest Common Factor Example : Find the HCF of 6 and 18. F6 = 1 and 6 2 and 3 F18 = 1 and 18 2 and 9 3 and 6 HCF = 6

  7. Factors Highest Common Factor Example : Find the HCF of 9 and 27. F9 = 1 and 9 3 and 3 F27 = 1 and 27 3 and 9 HCF = 9

  8. Factors Find the HCF for these terms • (a) 16 and 24 • 9 and 6 • 4 and 12 • 8 and 20 8 3 4 4

  9. Factors When finding the Highest Common Factor for algebraic terms, treat each part of the term separately Example Find the highest common factor of 4x and 24x Step 1 : Find the HCF of the first part of the term 4 Step 2 : Find what is common in the second part of the term x HCF = 4x Step 3 : Bring both terms together

  10. Factors When finding the Highest Common Factor for algebraic terms, treat each part of the term separately Example 2 Find the highest common factor of 6x and 9 Step 1 : Find the HCF of the first part of the term 3 Step 2 : Find what is common in the second part of the term Nothing common HCF = 3 Step 3 : Bring both terms together

  11. Factors Find the HCF for these terms • (a) 16x and 24x • 9s and 6s • 4h and 12 • 8x and 20x • (e) ab2 and a2b 8x 3s 4 4x ab

  12. Factorising Check by multiplying out the bracket to get back to where you started Example Factorise 3x + 15 1. Find HCF of 3x and 15, using 3 step method 3 1. HCF first part Nothing common 2. Common factor of second part 3 3. Bring both parts together to get HCF 2. HCF goes outside the bracket 3( ) 3. To see what goes inside the bracket, divide each initial term by the HCF 3x ÷ 3 = x 3( x + 5 ) 15 ÷ 3 = 5

  13. Factorising Check by multiplying out the bracket to get back to where you started Example Factorise 6x + 24 1. Find HCF of 6x and 24, using 3 step method 6 1. HCF first part Nothing common 2. Common factor of second part 6 3. Bring both parts together to get HCF 2. HCF goes outside the bracket 6( ) 3. To see what goes inside the bracket, divide each initial term by the HCF 6x ÷ 6 = x 6( x + 4 ) 24 ÷ 6 = 4

  14. Factorising Check by multiplying out the bracket to get back to where you started Example Factorise 8x + 12x 1. Find HCF of 8x and 12x, using 3 step method 4 1. HCF first part x 2. Common factor of second part 4x 3. Bring both parts together to get HCF 2. HCF goes outside the bracket 4x( ) 3. To see what goes inside the bracket, divide each initial term by the HCF 8x ÷ 4x = 2 4x( 2 + 3 ) 12x ÷ 4x = 3

  15. Factorising Check by multiplying out the bracket to get back to where you started Example Factorise 2x² + 4xy + 6x 1. Find HCF of 2x², 4xy and 6x using 3 step method 2 1. HCF first part x 2. Common factor of second part 2x 3. Bring both parts together to get HCF 2. HCF goes outside the bracket 2x( ) 3. To see what goes inside the bracket, divide each initial term by the HCF 2x² ÷ 2x = x 4xy ÷ 2x = 2y 6x ÷ 2x = 3 2x( x + 2y +3 )

  16. Factorising Factorise the following : 3(x + 2) • (a) 3x + 6 • 4xy – 2x • 6a + 7a2 • (d) xy2 -xy + 4x Be careful ! 2x(2y – 1) a(6 + 7a) x(y2 – y + 4)

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