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2.1 Factors and Multiples Part 2
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2.1 Factors and Multiples Part 2

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  • 1. 2.1 Factors and Multiples March 03, 2014 3.1FactorsandMultiplesofWholeNumbers Primenumbers =#thatcanonlybedividedby1anditself Examples: 1
  • 2. 2.1 Factors and Multiples March 03, 2014 Whenafactorofanumberhasexactlytwodivisors– 1anditself,thefactorisa primefactor . However,whencanexpressALLnumbersintermsofprimefactors. Wecallthis primefactorizationandwriteanumberasaproductofitsprimefactors. Thefactorsof12are1,2,3,4,6,and12. 12=2 2 3or2 . . 2 . 3 2
  • 3. 2.1 Factors and Multiples March 03, 2014 Thereare twomethodstoindtheprimefactorizationofanumber: Method1: FactorTrees Example1: Writetheprimefactorizationof2646. 3
  • 4. 2.1 Factors and Multiples March 03, 2014 Method2 : Userepeateddivision. STEP1: Beginbydividingthenumberbytheleast(smallest)primefactor. STEP2: Dividebythisprimefactoruntilitisnolongerafactor. STEP3: Chooseanotherprimefactorandcontinuewithsteps1and2. STEP4: Stopwhenthequotientreaches1. 4
  • 5. 2.1 Factors and Multiples March 03, 2014 Nowyoutry! Writetheprimefactorizationof3150. 5
  • 6. 2.1 Factors and Multiples For2ormorenaturalnumberswecandeterminetheir factor,thegreatestfactorthatallthenumbershavein March 03, 2014 greatest common common. Example2: DeterminetheGCFof126and144. Method1: Determineallthefactorsforeachnumber. 6
  • 7. 2.1 Factors and Multiples March 03, 2014 Method2: Findallthefactorsofonenumberandcheckwhichnumbersaredivisiblebythesecond. 7
  • 8. 2.1 Factors and Multiples March 03, 2014 Method3: Useprimefactorization. STEP1: STEP2: STEP3: Findtheprimefactorsofeachnumberusingprimefactorization. Determinewhichprimefactorsappearinbothnumbers. MultipletherepeatednumberstoindtheGCF. 8
  • 9. 2.1 Factors and Multiples March 03, 2014 9
  • 10. 2.1 Factors and Multiples March 03, 2014 Nowyoutry! FindtheGCFof234and342. 10
  • 11. 2.1 Factors and Multiples March 03, 2014 11
  • 12. 2.1 Factors and Multiples March 03, 2014 Whatarethemultiplesof22? Togeneratemultiplessimplymultiplyanumberbythe naturalnumbers(1,2,3,4...) For2ormorenaturalnumberswecandeterminetheir least commonmultiple ,thesmallestnumberthatisdivisibleby bothnumbers. Example3 : DeterminetheLCMof14,20,and42. 12
  • 13. 2.1 Factors and Multiples March 03, 2014 Method1: Listallthemultiplesofeachnumberuntilthesamenumberappearsinall3lists. 13
  • 14. 2.1 Factors and Multiples March 03, 2014 Method2: Listthemultiplesofthelargestnumberandchecktoseewhichnumbersaredivisiblebytheothernumbers. 14
  • 15. 2.1 Factors and Multiples March 03, 2014 Method3: Useprimefactorization. STEP1: Findtheprimefactorsofallofthenumbersusingprimefactorization. STEP2: Determinethegreatestpowerofalltheprimenumbersusedin STEP3: MultiplythegreatestpowerofeachprimefactortogettheLCM. anylist. 15
  • 16. 2.1 Factors and Multiples March 03, 2014 Nowyoutry! FindtheLCMof28,42,and63. 16
  • 17. 2.1 Factors and Multiples March 03, 2014 17