Transcript
2.1 Factors and Multiples
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3.1FactorsandMultiplesofWholeNumbers
Primenumbers=#thatcanonlybedividedby1anditself
Examples:
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Whenafactorofanumberhasexactlytwodivisors–1anditself,thefactorisa primefactor .
However,whencanexpressALLnumbersintermsofprimefactors.Wecallthis primefactorizationandwriteanumberasaproductofitsprimefactors.
Thefactorsof12are1,2,3,4,6,and12.
12=2 .2 .3or2 2 .3
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Thereare twomethodstoindtheprimefactorizationofanumber:
Method1:FactorTrees
Example1: Writetheprimefactorizationof2646.
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Method2 :Userepeateddivision.STEP1: Beginbydividingthenumberbytheleast(smallest)primefactor.STEP2: Dividebythisprimefactoruntilitisnolongerafactor.STEP3: Chooseanotherprimefactorandcontinuewithsteps1and2.STEP4: Stopwhenthequotientreaches1.
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Nowyoutry!Writetheprimefactorizationof3150.
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For2ormorenaturalnumberswecandeterminetheir greatest commonfactor,thegreatestfactorthatallthenumbershavein common.
Example2:DeterminetheGCFof126and144.
Method1:Determineallthefactorsforeachnumber.
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Method2:Findallthefactorsofonenumberandcheckwhichnumbersaredivisiblebythesecond.
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Method3:Useprimefactorization.STEP1: Findtheprimefactorsofeachnumberusingprimefactorization.STEP2: Determinewhichprimefactorsappearinbothnumbers.STEP3: MultipletherepeatednumberstoindtheGCF.
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Nowyoutry!FindtheGCFof234and342.
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Whatarethemultiplesof22?Togeneratemultiplessimplymultiplyanumberbythenaturalnumbers(1,2,3,4...)
For2ormorenaturalnumberswecandeterminetheir leastcommonmultiple ,thesmallestnumberthatisdivisiblebybothnumbers.
Example3 :DeterminetheLCMof14,20,and42.
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Method1:Listallthemultiplesofeachnumberuntilthesamenumberappearsinall3lists.
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Method2:Listthemultiplesofthelargestnumberandchecktoseewhichnumbersaredivisiblebytheothernumbers.
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Method3:Useprimefactorization.STEP1: Findtheprimefactorsofallofthenumbersusingprimefactorization.
STEP2: Determinethegreatestpowerofalltheprimenumbersusedin anylist.STEP3: MultiplythegreatestpowerofeachprimefactortogettheLCM.
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Nowyoutry!FindtheLCMof28,42,and63.
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