Question

escreva a fatoração completa dos seguintes números naturais ; a)80 b)98 c)128 d)164 e)132 F)162 G)180 h)240 I)342 J)625 E) 440 M)1000 N)1024 O)2.100

Answer 1

Resposta e xplicação passo a passo:

$a)\ 80\\80/2\\40/2\\20/2\\10/2\\5/5\\1\\\\2\bullet2\bullet2\bullet2\bullet5=2^4\bullet5=80\\\\\\b)\ 98\\98/2\\49/7\\7/7\\1\\\\2\bullet7\bullet7=2\bullet7^2=98\\\\\\c)\ 128\\128/2\\64/2\\32/2\\16/2\\8/2\\4/2\\2/2\\1\\\\2\bullet2\bullet2\bullet2\bullet2\bullet2\bullet2=2^7=128\\\\\\d)\ 164\\164/2\\82/2\\41/41\\1\\\\2\bullet2\bullet41=2^2\bullet41=164$

$e)\ 132\\132/2\\66/2\\33/3\\11/11\\1\\\\2\bullet2\bullet3\bullet11=2^2\bullet3\bullet11=132\\\\\\f)\ 162\\162/2\\81/3\\27/3\\9/3\\3/3\\1\\\\2\bullet3\bullet3\bullet3\bullet3=2\bullet3^4=162\\\\\\g)\ 180\\180/2\\90/2\\45/3\\15/3\\5/5\\1\\\\2\bullet2\bullet3\bullet3\bullet5=2^2\bullet3^2\bullet5=180\\\\\\h)\ 240\\240/2\\120/2\\60/2\\30/2\\15/3\\5/5\\1\\\\2\bullet2\bullet2\bullet2\bullet3\bullet5=2^4\bullet3\bullet5=240$

$i)\ 342\\342/2\\171/3\\57/3\\19/19\\1\\\\2\bullet3\bullet3\bullet19=2\bullet3^2\bullet19=342\\\\\\j)\ 625\\625/5\\125/5\\25/5\\5/5\\1\\\\5\bullet5\bullet5\bullet5=5^4=625$

$l)\ 440\\440/2\\220/2\\110/2\\55/5\\11/11\\1\\\\2\bullet2\bullet2\bullet5\bullet11=2^3\bullet5\bullet11=440\\\\\\m)\ 1000\\1000/2\\500/2\\250/2\\125/5\\25/5\\5/5\\1\\\\2\bullet2\bullet2\bullet5\bullet5\bullet5=2^3\bullet5^3=1000$

$n)\ 1024\\1024/2\\512/2\\256/2\\128/2\\64/2\\32/2\\16/2\\8/2\\4/2\\2/2\\1\\\\2\bullet2\bullet2\bullet2\bullet2\bullet2\bullet2\bullet2\bullet2\bullet2=2^{10}=1024$

$o)\ 2100\\2100/2\\1050/2\\525/3\\175/5\\35/5\\7/7\\1\\\\2\bullet2\bullet3\bullet5\bullet5\bullet7=2^2\bullet3\bullet5^2\bullet7=2100$