Question

7. Determinati cel mai mare divizor comun al următoarelor numere naturale: b) 30:45; 75: f72: 108: 144: a) 36:48:54: e) 75: 150, 200, c) 60; 48; 72; g) 70; 105; 245; d) 54; 72; 90; h) 80; 200; 360.
Va rog . Am nevoie urgent .​

Answer 1

Răspuns:

a) 36:48:54

36= 2²×3²

48= 2⁴×3

54= 2×3³

cmmdc(36,48,54) = 2×3 = 6

b) 30:45; 75

30= 2×3×5

45 = 3²×5

75 = 3×5²

cmmdc(30,45,75) = 3×5 = 15

c) 60; 48; 72

60= 2²×3×5

48= 2⁴×3

72= 2³×3²

cmmdc(60, 48, 72)= 2²×3 = 4×3 = 12

d) 54; 72; 90

54= 2×3³

72= 2³×3²

90= 2×3²×5

cmmdc(54,72,90)= 2×3² = 2×9 = 18

e) 75: 150, 200

75= 3×5²

150= 2×3×5²

200= 2³×5²

cmmdc(75,150,200)= 5² = 25

f)72: 108: 144

72= 2³×3²

108= 2²×3³

144= 2⁴×3²

cmmdc(72, 108, 144)= 2²×3² = 4×9= 36

g) 70; 105; 245

70= 2×5×7

105=3×5×7

245=5×7²

cmmdc(70,105,245)= 5×7 = 35

h) 80; 200; 360

80= 2⁴×5

200= 2³×5²

360= 2³×3²×5

cmmdc(80,200,360)= 2³×5 = 8×5 = 40