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H.C.F

H.C.F. Review The factors of 30 and 40?. 30 1 x 30 2 x 15 3 x 10 5 x 6  1,2,3,5,6,10,15, and 30 40 1 x 40 2 x 20 4 x 10 5 x 8  1,2,4,5,8,10,20, and 40. Highest Common Factor? 10. Prime factorisation. 30 = 2 x 3 x 5. 4 0 = 2 x 2 x 2 x 5.

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H.C.F

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  1. H.C.F

  2. ReviewThe factors of 30 and 40? 30 • 1 x 30 • 2 x 15 • 3 x 10 • 5 x 6 1,2,3,5,6,10,15, and 30 40 • 1 x 40 • 2 x 20 • 4 x 10 • 5 x 8 1,2,4,5,8,10,20, and 40 Highest Common Factor? 10

  3. Prime factorisation 30 = 2 x 3 x 5 40 = 2 x 2 x 2 x 5 HCF of 30 and 40 = 2 x 5 = 10

  4. Try..H.C.F. of 3a and 3b 3a = 3 x a 3b = 3 x b The H.C.F. of 3a and 3b is 3

  5. H.C.F. of 5a and 10 5a = 5 x a 10 = 2 x 5 The H.C.F. of 5a and 10 is 5

  6. p2 and 6p p2 = p x p 6p = 6 x p The H.C.F. of p2 and 6p is p

  7. H.C.F. 4m2 and 6m • 4m2 = 2 x 2 x m x m • 6m = 2 x 3 x m • The H.C.F. of 4m2 and 6m is 2 x m = 2m

  8. You may work odd or even numbers!Find the highest common factor of: • 2x and x • 24m and 12n • s and s2 • 2y and 2y2 • 12d and 6d2 • ab and ab2 • mn and m2n2 • 6a2b amd 12ab2 • pq and p2q2 • 4mn2 and 6m2n

  9. Factorisation A reverse of removing brackets

  10. Finding Common Factors • 1st step : find common variables • Example  18p and 4q • No variables in common • HCF of 18 and 4 2 • 18p+4q  2 (9p +2q)

  11. Factorise! 18s + 12t + 24u HCF = 6 6 (3s + 2t + 4u) 9pq – 6qr HCF = 3q 3q (3p – 2r) t2 – 2t HCF = t t (t-2)

  12. Factorise! ac + ad + bc + bd • Divide into pairs! ac + ad + bc + bd • a is common to the 1st pair • b is common to the 2nd pair • a ( c+d) + b (c+d) • c + d is common to both terms • Thus..we have (c+d)(a+b)

  13. 2mh + 3mk – 2nh – 3nk Pairs 2mh + 3mk – 2nh – 3nk m(2h + 3k)– n (2h +3k) 2h +3k are the same in both terms Thus we have : (m-n)(2h + 3k)

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