6. Determine o m.d.c. dos números:
a) 112 e 70
b) 90 e 225
c) 504 e 588
d) 39, 65 e 91
e) 144, 216 e 288
Pls me ajudem
Soluções para a tarefa
Resposta:
a) 560.
b) 450.
c) 3.528.
d) 1.365.
e) 864.
Explicação passo-a-passo:
a)
112, 70 | ÷ 2
56, 35 | ÷ 2
28, 35 | ÷ 2
14, 35 | ÷ 2
7, 35 | ÷ 5
7, 7 | ÷ 7
1, 1 | 2 · 2 · 2 · 2 · 5 · 7 = 560.
b)
90, 225 | ÷ 2
45, 225 | ÷ 3
15, 75 | ÷ 3
5, 25 | ÷ 5
1, 5 | ÷ 5
1, 1 | 2 · 3 · 3 · 5 · 5 = 450.
c)
504, 588 | ÷ 2
252, 294 | ÷ 2
126, 147 | ÷ 2
63, 147 | ÷ 3
21, 49 | ÷ 3
7, 49 | ÷ 7
1, 7 | ÷ 7
1, 1 | 2 · 2 · 2 · 3 · 3 · 7 · 7 = 3.528.
d)
39, 65 e 91 | ÷ 3
13, 65, 91 | ÷ 5
13, 13, 91 | ÷ 7
13, 13, 13 | ÷ 13
1, 1, 1 | 3 · 5 · 7 · 13 = 1.365.
e)
144, 216 e 288 | ÷ 2
72, 108, 144 | ÷ 2
36, 54, 72 | ÷ 2
18, 27, 36 | ÷ 2
9, 27, 18 | ÷ 2
9, 27, 9 | ÷ 3
3, 9, 3 | ÷ 3
1, 3, 1 | ÷ 3
1, 1, 1 | 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 = 864.
Resposta:
a)14
b)45
c)84
d)13
e)72
Explicação passo-a-passo:
a) 112,70| 2
56,35| 2
28,35| 2
14,35| 2
7, 35| 5
7, 7| 7
1, 1|2.7= 14
b) 90,225| 2
45,225| 3
15,75| 3
5,25| 5
1,5| 5
1,1| 3.3.5=45
c)504| 2 508| 2
252| 2 294| 2
126| 2 147| 3
63| 3 49| 3
21| 3 7| 7
7| 7 1
1
2.2.2.3.3.7 2.2.3.3.7
2.2.3.7=4.21=84
d)39,65,92| 3
13,65,91| 5
13,13,91| 7
13,13,13| 13
1, 1, 1 |=13
e)144,216,288| 2
72,108,144| 2
36,54,72| 2
18,27,36| 3
6, 9, 12| 3
2, 3, 4| 2.2.2.3.3=72