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2.1 Factors and Multiples Part 2

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2.1 Factors and Multiples Part 2

1. 1. 2.1 Factors and Multiples March 03, 2014 3.1FactorsandMultiplesofWholeNumbers Primenumbers =#thatcanonlybedividedby1anditself Examples: 1
2. 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. 3. 2.1 Factors and Multiples March 03, 2014 Thereare twomethodstoindtheprimefactorizationofanumber: Method1: FactorTrees Example1: Writetheprimefactorizationof2646. 3
4. 4. 2.1 Factors and Multiples March 03, 2014 Method2 : Userepeateddivision. STEP1: Beginbydividingthenumberbytheleast(smallest)primefactor. STEP2: Dividebythisprimefactoruntilitisnolongerafactor. STEP3: Chooseanotherprimefactorandcontinuewithsteps1and2. STEP4: Stopwhenthequotientreaches1. 4
5. 5. 2.1 Factors and Multiples March 03, 2014 Nowyoutry! Writetheprimefactorizationof3150. 5
6. 6. 2.1 Factors and Multiples For2ormorenaturalnumberswecandeterminetheir factor,thegreatestfactorthatallthenumbershavein March 03, 2014 greatest common common. Example2: DeterminetheGCFof126and144. Method1: Determineallthefactorsforeachnumber. 6
7. 7. 2.1 Factors and Multiples March 03, 2014 Method2: Findallthefactorsofonenumberandcheckwhichnumbersaredivisiblebythesecond. 7
8. 8. 2.1 Factors and Multiples March 03, 2014 Method3: Useprimefactorization. STEP1: STEP2: STEP3: Findtheprimefactorsofeachnumberusingprimefactorization. Determinewhichprimefactorsappearinbothnumbers. MultipletherepeatednumberstoindtheGCF. 8
9. 9. 2.1 Factors and Multiples March 03, 2014 9
10. 10. 2.1 Factors and Multiples March 03, 2014 Nowyoutry! FindtheGCFof234and342. 10
11. 11. 2.1 Factors and Multiples March 03, 2014 11
12. 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. 13. 2.1 Factors and Multiples March 03, 2014 Method1: Listallthemultiplesofeachnumberuntilthesamenumberappearsinall3lists. 13
14. 14. 2.1 Factors and Multiples March 03, 2014 Method2: Listthemultiplesofthelargestnumberandchecktoseewhichnumbersaredivisiblebytheothernumbers. 14
15. 15. 2.1 Factors and Multiples March 03, 2014 Method3: Useprimefactorization. STEP1: Findtheprimefactorsofallofthenumbersusingprimefactorization. STEP2: Determinethegreatestpowerofalltheprimenumbersusedin STEP3: MultiplythegreatestpowerofeachprimefactortogettheLCM. anylist. 15
16. 16. 2.1 Factors and Multiples March 03, 2014 Nowyoutry! FindtheLCMof28,42,and63. 16
17. 17. 2.1 Factors and Multiples March 03, 2014 17