Question

Dois números cujo mdc seja 5 *


10,12
10,15
5,8
20,27
Outro:

Answer 1

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$\sf\large\green{\boxed{\blue{ \ \ \ M.D.C. (10, 15) = 5 \ \ \ }}}$

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$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O\ PASSO{-}A{-}PASSO\ \ \ }}$✍

❄☃ $\sf(\gray{+}\ \red{cores}\ \blue{com}\ \pink{o}\ \orange{App}\ \green{Brainly})$ ☘☀

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☺lá, Samilly,  como tens passado nestes tempos de quarentena⁉ E os estudos à distância, como vão⁉ Espero que bem❗

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☔ Acompanhe a resolução abaixo, feita através de algumas manipulações algébricas, e após o resultado você encontrará um link com mais informações sobre

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✈ M.D.C.;

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que talvez te ajude com exercícios semelhantes no futuro. ✌

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10,12

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$Fat(10)\\\\ \left[\begin{array}{ccc}10&/2& = 5\\\\5&/5 &= 1\\\end{array}\right]\\\\\\ Fat(10) = 2 \cdot 5 \cdot 1\\\\\\Fat(12)\\\\ \left[\begin{array}{ccc}12&/2& = 6\\\\6&/2 &= 3\\\\3&/3 &= 1\\\end{array}\right]\\\\\\ Fat(12) = 2 \cdot 2 \cdot 3 \cdot 1\\\\\\\dfrac{Fat(10)}{Fat(12)} = \dfrac{2 \cdot 5 \cdot 1}{2 \cdot 2 \cdot 3 \cdot 1} = \dfrac{5}{2 \cdot 3} \cdot \dfrac{2}{2} = \boxed{ \ \dfrac{5}{6} \ } \cdot \dfrac{2}{2}$

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$\sf\large\green{\boxed{\blue{ \ \ \ M.D.C. (10, 12) = 2 \ \ \ }}}$ ❌

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10,15

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$Fat(10)\\\\ \left[\begin{array}{ccc}10&/2& = 5\\\\5&/5 &= 1\\\end{array}\right]\\\\\\ Fat(10) = 2 \cdot 5 \cdot 1\\\\\\Fat(15)\\\\ \left[\begin{array}{ccc}15&/3& = 5\\\\5&/5 &= 1\\\end{array}\right]\\\\\\ Fat(15) = 3 \cdot 5 \cdot 1\\\\\\\dfrac{Fat(10)}{Fat(15)} = \dfrac{2 \cdot 5 \cdot 1}{3 \cdot 5 \cdot 1} = \dfrac{2}{3} \cdot \dfrac{5}{5} = \boxed{ \ \dfrac{2}{3} \ } \cdot \dfrac{5}{5}$

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$\sf\large\green{\boxed{\blue{ \ \ \ M.D.C. (10, 15) = 5 \ \ \ }}}$ ✅

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5,8

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$Fat(5)\\\\ \left[\begin{array}{ccc}5&/5& = 1\\\end{array}\right]\\\\\\ Fat(5) = 5 \cdot 1\\\\\\Fat(8)\\\\ \left[\begin{array}{ccc}8&/2& = 4\\\\4&/2 &= 2\\\\2&/2 &= 1\\\end{array}\right]\\\\\\ Fat(8) = 2 \cdot 2 \cdot 2 \cdot 1\\\\\\\dfrac{Fat(5)}{Fat(8)} = \dfrac{5 \cdot 1}{2 \cdot 2 \cdot 2 \cdot 1} = \dfrac{5}{2 \cdot 2 \cdot 2} \cdot \dfrac{1}{1} = \boxed{ \ \dfrac{5}{8} \ } \cdot \dfrac{1}{1}$

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$\sf\large\green{\boxed{\blue{ \ \ \ M.D.C. (5, 8) = 1 \ \ \ }}}$ ❌

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20,27

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$Fat(20)\\\\ \left[\begin{array}{ccc}20&/2& = 10\\\\10&/2 &= 5\\\\5&/5 &= 1\\\end{array}\right]\\\\\\ Fat(20) = 2 \cdot 2 \cdot 5 \cdot 1\\\\\\Fat(27)\\\\ \left[\begin{array}{ccc}27&/3& = 9\\\\9&/3 &= 3\\\\3&/3 &= 1\\\end{array}\right]\\\\\\ Fat(27) = 3 \cdot 3 \cdot 3 \cdot 1\\\\\\\dfrac{Fat(20)}{Fat(27)} = \dfrac{2 \cdot 2 \cdot 5 \cdot 1}{3 \cdot 3 \cdot 3 \cdot 1} = \dfrac{2 \cdot 2 \cdot 5}{3 \cdot 3 \cdot 3} \cdot \dfrac{1}{1} = \boxed{ \ \dfrac{20}{27} \ } \cdot \dfrac{1}{1}$

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$\sf\large\green{\boxed{\blue{ \ \ \ M.D.C. (20, 27) = 1 \ \ \ }}}$ ❌

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✈  M.D.C. (https://brainly.com.br/tarefa/35395541)

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_______________________________☁

☕ Bons estudos.

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