Question

9. Uma fatoração do número 1200 é 2ª X x 3 x 5°. Qual é o valor de a + b + c?​

Answer 1

$\Large\boxed{\begin{array}{l}\begin{array}{c|c}\sf1200&\sf2\\\sf600&\sf2\\\sf300&\sf2\\\sf150&\sf2\\\sf75&\sf3\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 1200=2^4\times3\times5^2\\\sf 1200=2^a\times3^b\times5^c\\\sf como\,1200=1200\,podemos\,escrever:\\\sf 2^a\times3^b\times5^c=2^4\times3\times5^2\\\sf DA\acute I\\\sf 2^a=2^4\implies a=4\\\sf 3^b=3\implies b=1\\\sf 5^c=5^2\implies c=2\\\sf a+b+c=4+1+2=7\checkmark\end{array}}$