Question

quais sao os divisores de 96

Answer 1

$\large\begin{array}{l} \texttt{Encontrar os divisores de 96.}\\\\\\ \texttt{Primeiramente, decomponha 96 em fatores primos:}\\\\ \begin{array}{r|l} \mathtt{96}&\mathtt{2}\\ \mathtt{48}&\mathtt{2}\\ \mathtt{24}&\mathtt{2}\\ \mathtt{12}&\mathtt{2}\\ \mathtt{6}&\mathtt{2}\\ \mathtt{3}&\mathtt{3}\\ \mathtt{1}& \end{array}\qquad\Rightarrow~\mathtt{96=2^5\cdot 3} \end{array}$

$\large\begin{array}{l} \texttt{Como se pode notar, os \'unicos fatores primos de 96 s\~ao}\\ \texttt{2 e 3.}\\\\\texttt{O expoente do 2 \'e 5, e o expoente do 3 \'e 1.}\\\\ \texttt{Os divisores de 96 ser\~ao todos os resultados que se}\\ \texttt{pode obter com esses dois n\'umeros, apenas variando os}\\ \texttt{expoentes.} \end{array}$

$\large\begin{array}{l} \bullet~~\texttt{expoente do 2:~~de 0 a 5.}\\ \bullet~~\texttt{expoente do 3:~~de 0 a 1.} \end{array}$


$\large\begin{array}{l} \texttt{Encontrando os divisores:}\\\\ \mathtt{2^0\cdot 3^0=1\cdot 1=1}\\\\ \mathtt{2^0\cdot 3^1=1\cdot 3=3}\\\\ \mathtt{2^1\cdot 3^0=2\cdot 1=2}\\\\ \mathtt{2^1\cdot 3^1=2\cdot 3=6}\\\\ \mathtt{2^2\cdot 3^0=4\cdot 1=4}\\\\ \mathtt{2^2\cdot 3^1=4\cdot 3=12}\\\\ \mathtt{2^3\cdot 3^0=8\cdot 1=8}\\\\ \mathtt{2^3\cdot 3^1=8\cdot 3=24}\\\\ \mathtt{2^4\cdot 3^0=16\cdot 1=16} \end{array}$

$\large\begin{array}{l} \mathtt{2^4\cdot 3^1=16\cdot 3=48}\\\\ \mathtt{2^5\cdot 3^0=32\cdot 1=32}\\\\ \mathtt{2^5\cdot 3^1=32\cdot 3=96} \end{array}$


$\large\begin{array}{l} \texttt{Agora, colocamos os divisores em ordem:}\\\\ \mathtt{D(96)=\{1,\,2,\,3,\,4,\,6,\,8,\,12,\,16,\,24,\,32,\,48,\,96\}}\\\\ \texttt{Este \'e o conjunto dos divisores de 96.} \end{array}$


$\large\begin{array}{l} \texttt{D\'uvidas? Comente.}\\\\ \texttt{Bons estudos!} \end{array}$