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Unit6:Section8.1FactorsandGreatestCommonFactors Numbersthataremultipliedtofindaproductarecalledfactors.Thesefactorsare whatthoseproductsaredivisibleby. Primefactorizationisfindingthefactorsofanumberthatareallprime.Basically,it isbreakingdownanumberintoitssimplestparts. EX:Findtheprimefactorizationof60. -Createaβnumbertreeβtofindalltheprimefactors. 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. 3π₯ ! πππ 6π₯ ! 3π₯ ! : 3 β π₯ β π₯ β π₯ 6π₯ ! : 3 β 2 β π₯ β π₯ GCF:3π₯ ! b. 4π₯ ! πππ 5π¦ ! 4π₯ ! : 4 β π₯ β π₯ β π₯ 5π¦ ! : 5 β π¦ β π¦ GCF:1 c. 12π₯ ! πππ 18π₯ ! 12π₯ ! : 2 β 2 β 3 β π₯ β π₯ β π₯ β π₯ 18π₯ ! : 3 β 3 β 2 β π₯ β π₯ GCF:6π₯ ! 8.1ExitSlip 1.PrimeFactorizationof100 2.FindtheGCFof30and40 3.FindtheGCFof32π₯π¦ ! πππ 20π₯ ! π¦ !