年7月录屏8数学

GRE数学备考（二）18主讲人：Celine算术部分的基本问题1.正整数n有奇数个因子，则n为完全平方数

2.因子个数求解公式：将整数n分解为质因子乘积形式,然后将每个质因子的幂分别加一相乘.n=a*a*a*b*b*c则因子个数=(3+1)(2+1)(1+1)eg.200=2*2*2*5*5因子个数=(3+1)(2+1)=12个3.能被8整除的数，后三位的和能被8整除能被9整除的数，各位数的和能被9整除.能被3整除的数，各位数的和能被3整除.计算的基本知识整数Whenintegersaremultiplied,eachofthemultipliedintegersiscalledafactorordivisoroftheresultingproduct.Forexample,so2,3,and10are(2)(3)(10)=60,factorsof60.Theleastcommonmultipleoftwononzerointegersaandbistheleastpositiveintegerthatisamultipleofbothaandb.Forexample,theleastcommonmultipleof30and75is150.Thegreatestcommondivisor(orgreatestcommonfactor)oftwononzerointegersaandbisthegreatestpositiveintegerthatisadivisorofbothaandb.d15,andthegreatestoftheseis15.Whenanintegeraisdividedbyanintegerb,wherebisadivisorofa,theresultisalwaysadivisorofa.Forexample,when60isdividedby6(oneofitsdivisors),theresultis10,whichisanotherdivisorof60.Aprimenumberisanintegergreaterthan1thathasonlytwopositivedivisors:1anditself.Thefirsttenprimenumbersare2,3,5,7,11,13,17,19,23,and29.primedivisors.Suchanexpressioniscalledaprimefactorization.Hereareseveralexamplesofprimefactorizations.212=(2)(2)(3)=(2)(3)14=(2)(7)481=(3)(3)(3)(3)=32338=(2)(13)(13)=(2)(13)52800=(2)(2)(2)(2)(2)(5)(5)=(2)(5)1,155=(3)(5)(7)(11)Anintegergreaterthan1thatisnotaprimenumberiscalledacompositenumber.Thefirsttencompositenumbersare4,6,8,9,10,12,14,15,16,and18.

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