Greatest common factor - GCF4 .2

VocabularyCommon Factor - Acommon factor is awhole numberthat is a factor of two or more non -zeroWholenumbersGreatest Common Factor (GCF )- the greatest wholenumber that is a factor of two or more non -zerowhole numberRelatively Prime - Two or morenumbers are relativelyprime if their greatest common factoris 1

Ex' Finding the GCF

Ahigh school asks forvolunteers to help deanUp local highways on one Saturday .each month .The group of volunteers has27 freshman, 18sophomores,36 juniors 45 seniors .What isthe greatest # of groups thatcan be formedif each group has the same number of eachtype of student? How many freshman,sophomore,juniors,andseniors will be in each group? '

Method 1 : Factor Ts

- 27 o 451127

39" 31IS2 . 11813 /12 go

Toto

agroupsw / 3 freshman 2 sopomores 4 junior 5 seniors

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Method2 - Factor trees

. 9 3 6 3 9 4 Is 3end

3 3 3 3 22. s .

Dr[27 3 .3 .3 in common : 3 .3 = q* I off12 .3 .3(36 2 .2 .3 .3 27 +9 =3 freshman18 + 9 =2 sophomores45 3 3 .5 36-94 juniors45 + 9=5 seniorsYour turnFind the greatest common factor of54 and 81 - 54 &-54 . El 6 4. a 9.

RI 3 I NA3 2 3 3 3 3 3 3

54 2 .3 .3 .3 3 .3 .3 = 67813 .3.3 .3Lame

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Ex² Identity ing relatively primeFind the greatestcommon factor of thenumbersThen tet ! Whether the numbers are relativelyprime.1) 28,63

- 28 Ism

22 . 3

GCF is28 : 2 .2 . 663 : 3 .3 . 0

2 )42,55- 42 7 - not relativelyi prime

55

76

3

42 :2 ,3 ,755 :5 .11 no common factors (otherthan 1)RELATIVELY RIME

Your Turn.3 ) .30,49

V :30 . 49 4 ).52 , 18

52 70

2 :26 . 23977

natrelativelyprime. 10 3

52 . 30:2,3,5/649: 7,7 l . 13 2 .52: 2 .2 . 1378 0.3 13 3 13 h2.13 :26)

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Ex³ Finding the GCF of monomials

Find the greatest common factor

16x2y å26x²y3

16 x² y 26x²y3

B 13 2

22222 2 0.0 2 13.(*.( VYYGCF :2x²y

Your Turn :- 12x3 18x² 40xy² 24ky

12x3 18x2 40x y3 .. .24 y y

6 362 2 20

2 3 2 10 . 32 22

25.32

(2.2. Arx 2.33 2.0

2 .3.x26x² (2.0.0 stbyyy2 -2-2:3. 6.

2 .2.2 % y8xy