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# 2.1 Factors and Multiples Part 1

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### 2.1 Factors and Multiples Part 1

1. 1. 2.1 Factors and Multiples Part 1 February 28, 2014 3.1FactorsandMultiplesofWholeNumbers Primenumbers =#thatcanonlybedividedby1anditself Examples: 1
2. 2. 2.1 Factors and Multiples Part 1 February 28, 2014 Whenafactorofanumberhasexactlytwodivisors– 1anditself,thefactorisa primefactor . However,whencanexpressALLnumbersintermsofprimefactors. Wecallthis primefactorizationandwriteanumberasaproductofitsprimefactors. Thefactorsof12are1,2,3,4,6,and12. 12=2 2 3or2 . . 2 . 3 2
3. 3. 2.1 Factors and Multiples Part 1 February 28, 2014 Thereare twomethodstoindtheprimefactorizationofanumber: Method1: FactorTrees Example1: Writetheprimefactorizationof2646. 3
4. 4. 2.1 Factors and Multiples Part 1 February 28, 2014 Method2 : Userepeateddivision. STEP1: Beginbydividingthenumberbytheleast(smallest)primefactor. STEP2: Dividebythisprimefactoruntilitisnolongerafactor. STEP3: Chooseanotherprimefactorandcontinuewithsteps1and2. STEP4: Stopwhenthequotientreaches1. 4
5. 5. 2.1 Factors and Multiples Part 1 February 28, 2014 Nowyoutry! Writetheprimefactorizationof3150. 5
6. 6. 2.1 Factors and Multiples Part 1 February 28, 2014 For2ormorenaturalnumberswecandeterminetheir greatest commonfactor,thegreatestfactorthatallthenumbershavein common. Example2: DeterminetheGCFof126and144. Method1: Determineallthefactorsforeachnumber. 6
7. 7. 2.1 Factors and Multiples Part 1 February 28, 2014 Method2: Findallthefactorsofonenumberandcheckwhichnumbersaredivisiblebythesecond. 7
8. 8. 2.1 Factors and Multiples Part 1 February 28, 2014 Method3: Useprimefactorization. STEP1: STEP2: STEP3: Findtheprimefactorsofeachnumberusingprimefactorization. Determinewhichprimefactorsappearinbothnumbers. MultipletherepeatednumberstoindtheGCF. 8
9. 9. 2.1 Factors and Multiples Part 1 February 28, 2014 9