Question

Calcule o MDC de
A) 72 é 108
B) 90 e 60
C) 6 é 35
D) 12, 18 e 30

Answer 1

O MDC de cada caso, é:

• A) = 36
• B) = 30
• C) = 1
• D) = 6

.MDC (Máximo Divisor Comum).

• Resolução:

$\sf A) \: mdc \: (72,108) \red{= 36}$

$\red{\sf{2,3,5,7...}}$

$\blue{\sf{\begin{array}{r|l}72,108&\red{\boxed{\blue{2}}}\\36,54&\red{\boxed{\blue{2}}}\\18,27&2\\9,27&\red{\boxed{\blue{3}}}\\3,9&\red{\boxed{\blue{3}}}\\1,3&3\\1,1\end{array}}}$

$\sf 2.2.3.3 = \red{\boxed{\blue{\sf{36}}}}$

$\sf B) \: mdc \: (90,60) \red{= 30}$

$\blue{\sf{\begin{array}{r|l}90,60&\red{\boxed{\blue{2}}}\\45,30&2\\45,15&\red{\boxed{\blue{3}}}\\15,5&3\\5,5&\red{\boxed{\blue{5}}}\\1,1\end{array}}}$

$\sf 2.3.5 = \red{\boxed{\blue{\sf{30}}}}$

$\sf C) \: mdc \: (6,35) \red{= 1}$

$\blue{\sf{\begin{array}{r|l}6,35&2\\3,35&3\\1,35&5\\1,7&7\\1,1\end{array}}}$

$\red{\boxed{\blue{\sf{1}}}}$

$\sf D) \: mdc \: (12,18,30) \red{= 6}$

$\blue{\sf{\begin{array}{r|l}12,18,30&\red{\boxed{\blue{2}}}\\6,9,15&2\\3,9,15&\red{\boxed{\blue{3}}}\\1,3,5&3\\1,1,5&5\\1,1,1\end{array}}}$

$\sf 2.3 = \red{\boxed{\blue{\sf{6}}}}$

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Bons estudos...

E espero ter ajudado!✏

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