Question

calcule o MDC dos numeros usando a decomposição individual : a) mdc de 135 e 54
b) mdc de 32 e 84
c) mdc de 36 e 84
d) mdc de 94 e 144​

Answer 1

Resposta:

Explicação passo-a-passo:

$\begin{array}{rr|c|c} & & MMC & MDC \\32, & 84 & 2 & 2\\ 16, & 42 & 2 & 2\\ 8, & 21 & 2\\ 4, & 21 & 2\\ 2, & 21 & 2\\ 1, & 21 & 3\\ 1, & 7 & 7\\ 1, & 1\\ \end{array}\\ MMC\,\,\ 2^5 \cdot 3 \cdot 7 = 672\\ MDC\,\,\ 2^2 = 4$

$\begin{array}{rr|c|c} & & MMC & MDC \\36, & 84 & 2 & 2\\ 18, & 42 & 2 & 2\\ 9, & 21 & 3 & 3\\ 3, & 7 & 3\\ 1, & 7 & 7\\ 1, & 1\\ \end{array}\\ MMC\,\,\ 2^2 \cdot 3^2 \cdot 7 = 252\\ MDC\,\,\ 2^2 \cdot 3 = 12$

$\begin{array}{rr|c|c} & & MMC & MDC \\94, & 144 & 2 & 2\\ 47, & 72 & 2\\ 47, & 36 & 2\\ 47, & 18 & 2\\ 47, & 9 & 3\\ 47, & 3 & 3\\ 47, & 1 & 47\\ 1, & 1\\ \end{array}\\ MMC\,\,\ 2^4 \cdot 3^2 \cdot 47 = 6768\\ MDC\,\,\ 2 = 2$