Question

determinati cel mai mare divizor comun al urmatoarelor nr nat a)36;48:54 b)30;45;75 c)60;48;72

Answer 1

a)36 = 4 × 9 = 2² × 3²

48 = 6 × 8 = 2 × 3 × 2³ = 2⁴ × 3

54 = 9 × 6 = 2 × 3 × 3 × 3 = 2 × 3³

Se iau toți factorii primi comuni, la puterile cele mai mici.

cmmdc = 2 × 3 = 6

b)30 = 2 × 15 = 2 × 3 × 5

45 = 9 × 5 = 3² × 5

75 = 3 × 25 = 3 × 5²

cmmdc = 15

c)60 =6 × 10 = 2 × 3 × 2 × 5 =2²×3 × 5

48 =  6 × 8 = 2 × 3 × 2³ = 2⁴ × 3

72 = 2³ × 3²

cmmdc = 2² × 3 = 12

Answer 2

a) 36 = 2²*3²

48 = 2^4 * 3

54 = 2 * 3^3

(36,48,54) = 2*3 = 6

b) 30 = 2*3*5

45 = 5*3²

75 = 3*5²

(30,45,75) = 3*5 = 15

c) 60 = 2² * 5 * 3

48 = 2^4 * 3

72 = 2^3 * 3²

(60,48,72) = 2² * 3 = 4*3 = 12

"^" inseamna "la puterea"