Download Unit 6: Section 8.1 Factors and Greatest Common Factors Numbers

Unit6:Section8.1FactorsandGreatestCommonFactors
Numbersthataremultipliedtofindaproductarecalledfactors.Thesefactorsare
whatthoseproductsaredivisibleby.
Primefactorizationisfindingthefactorsofanumberthatareallprime.Basically,it
isbreakingdownanumberintoitssimplestparts.
EX:Findtheprimefactorizationof60.
-Createa‘numbertree’tofindalltheprimefactors.
60:
1,60
2,30
3,10
5,2 PrimeFactors:2,3,5,2
Factorsthataresharedbetweentwoormorewholenumbersarecalledcommon
factors.Thegreatestofthesecommonfactorsiscalledthegreatestcommonfactor
orGCF.
FindtheGCFofeachpairofnumbers.
a. 24and60
i. Factorsof24:1,24,2,12,3,8,4,6
ii. Factorsof60:1,60,2,30,3,20,4,15,5,12,6,10,
iii. GCF:12
b. 18and27
i. Factorsof18:1,18,2,9,3,6
ii. Factorsof27:1,27,3,9,
iii. GCF:9
(AnothermethodoffindingtheGCFistouseprimefactorization).
18: 27:
1,18 1,27
2,9 3,9
3,3 3,3
FindingtheGCFofmonomials:
a. 3𝑥 ! 𝑎𝑛𝑑 6𝑥 ! 3𝑥 ! : 3 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥
6𝑥 ! : 3 ∙ 2 ∙ 𝑥 ∙ 𝑥
GCF:3𝑥 ! b. 4𝑥 ! 𝑎𝑛𝑑 5𝑦 ! 4𝑥 ! : 4 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥
5𝑦 ! : 5 ∙ 𝑦 ∙ 𝑦
GCF:1
c. 12𝑥 ! 𝑎𝑛𝑑 18𝑥 ! 12𝑥 ! : 2 ∙ 2 ∙ 3 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥
18𝑥 ! : 3 ∙ 3 ∙ 2 ∙ 𝑥 ∙ 𝑥
GCF:6𝑥 ! 8.1ExitSlip
1.PrimeFactorizationof100
2.FindtheGCFof30and40
3.FindtheGCFof32𝑥𝑦 ! 𝑎𝑛𝑑 20𝑥 ! 𝑦 !