Question

Qual o mdc ( 9;36;54 )
Qual o mdc ( 20; 60; 100 )
Qual o mdc ( 180; 132; 108 )

Answer 1

D(9) = {1, 3, 9}
D(36) = {1, 2, 3, 4, 6, 9, 12, 18, 36}
D(54) = {1, 2, 3, 6, 9, 18, 27, 54}

MDC (9,36,54) = 9

D(20) = {1, 2, 4, 5, 10, 20}
D(60) = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}
D(100) = {1, 2, 4, 5, 10, 20, 25, 50, 100}

MDC (20,60,100) = 20

D(180) = {1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180}
D(132) = {1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 }
D(108) = {1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 }

MDC (180,132,108) = 12

Answer 2

Para tirar o MDC teremos que fatorar ambos separadamente e multiplicar os termos em comum .

MDC ( 9;36;54 )

9|3    36|3    54|3
3|3    12|2    18|3
1        6|2      6|3
          3|3      2|2
          1         1

Fatores comuns: 3²
$\boxed{ 3^{2} = 9 }$

MDC ( 20; 60; 100 )

20|2   60|2     100|2
10|2   30|2      50|2
5|5     15|3      25|5
1        5|5         5|5
          1            1
Fatores comuns : 2² e 5 
$\boxed{ 2^{2} *5=20}$

MDC ( 180; 132; 108 )

180|2   132|2         108|2
90|2       66|2         54|2
45|3      33|3           27|3
15|3      11|11          9|3
5|5         1                3|3
1                             1

Fatores comuns : 2² e 3
$\boxed{ 2^{2} *3= 12}$