Question

2. Calcule o mdc pelo processo da decomposi¸c˜ao em
fatores primos.
a) 24 e 32
b) 18 e 15
c) 18, 60 e 24
d) 12 e 25

Answer 1

$\Large\boxed{\begin{array}{l}\tt a)\\\begin{array}{c|c}\sf24&\sf2\\\sf12&\sf2\\\sf6&\sf2\\\sf3&\sf3\\\sf1\end{array}\\\sf 24=2^3\cdot3\\\begin{array}{c|c}\sf32&\sf2\\\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}\\\sf 32=2^5\\\sf m\cdot d\cdot c~ \acute e~o~produto~dos~fatores~primos~comuns\\\sf tomados~ao~menor~expoente\\\sf m\cdot d\cdot c(24,32)=2^3=8\end{array}}$

$\Large\boxed{\begin{array}{l}\tt b)\\\begin{array}{c|c}\sf18&\sf2\\\sf 9&\sf3\\\sf 3&\sf3\\\sf1\end{array}\\\sf 18=2\cdot3^2\\\begin{array}{c|c}\sf15&\sf3\\\sf 5&\sf5\\\sf1\end{array}\\\sf 15=3\cdot5\\\sf m\cdot d\cdot c~ \acute e~o~produto~dos~fatores~primos~comuns\\\sf tomados~ao~menor~expoente\\\sf m\cdot d\cdot c(18,15)=3\end{array}}$

$\boxed{\begin{array}{l}\tt c)\\\begin{array}{c|c}\sf18&\sf2\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 18=2\cdot3^2\\\begin{array}{c|c}\sf60&\sf2\\\sf 30&\sf2\\\sf15&\sf3\\\sf5&\sf5\\\sf1\end{array}\\\sf60=2^2\cdot3\cdot5\\\begin{array}{c|c}\sf24&\sf2\\\sf12&\sf2\\\sf6&\sf2\\\sf3&\sf3\\\sf1\end{array}\\\sf 24=2^3\cdot3\end{array}}$

$\Large\boxed{\begin{array}{l}\sf m\cdot d\cdot c~ \acute e~o~produto~dos~fatores~primos~comuns\\\sf tomados~ao~menor~expoente\\\sf m\cdot d\cdot c(18,60,24)=2\cdot3=6\end{array}}$

$\Large\boxed{\begin{array}{l}\tt d)\\\begin{array}{c|c}\sf12&\sf2\\\sf6&\sf2\\\sf3&\sf3\\\sf1\end{array}\\\sf 12=2^2\cdot3\\\begin{array}{c|c}\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf25=5^2\\\sf m\cdot d\cdot c~ \acute e~o~produto~dos~fatores~primos~comuns\\\sf tomados~ao~menor~expoente\\\sf m\cdot d\cdot c(12,25)=1\end{array}}$

Answer 2

Resposta:

a) 24 e 32:

24,32: 2

12,16: 2

6,8: 2

3,4: 2

3,2: 2

3,1: 3

------------

1,1 = 2.2.2 = 8

Resp: 8

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b) 18 e 15

18,15: 2

9,15: 3

3,5: 3

1,5: 5

-----------------

1,1 = 3

Resp.: 3

*********************

c) 18, 60 e 24

18,60,24: 2

9,30,12: 2

9,15,6: 2

3,15,3: 3

1,5,1: 5

---------------

1,1,1 = 2.3 = 6

Resp.: 6

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d) 180, 36 e 120

180,36,120: 2

90,18,60: 2

45,9,30: 2

45,9,15: 3

15,3,5: 3

5,1,5: 5

--------------------

1,1,1 = 2.2.3 = 4.3 = 12

Resp.: 12

********************************************

e) 12 e 15

12,15: 2

6,15: 2

3,15: 3

1,5: 5

-------------

1,1 = 3

Resp.: 3

*********************************

f) 7 e 18

7,18: 2

7,9: 3

7,3: 3

7,1: 7

-----------

1,1 = 1

Resp.: 1

Explicação passo-a-passo:

espero ter ajudado boa sorte no exercício