Question

numerele 127,53,76 impartite la acelasi numar nenul n dau rsesturile 7,5 si respectiv 4.Det numarul nat n

Answer 1

127÷n=C₁ r 7   ⇒ 
53÷n=C₂ r 5     ⇒ 
76÷n=C₃ r 4     ⇒  
n= (127-7) ÷ C₁ ⇒ 
n= (53-5 ) ÷ C₂  ⇒
n= (76-4 ) ÷ C₃  ⇒
n=120 ÷ C₁ ⇒
n= 48 ÷ C₂  ⇒
n= 72 ÷ C₃  ⇒
n| 120
n| 48      ⇒ n|720 ⇒ n= (1,2,3,4,5,6,8,9,10,...,720)
n| 72   
c.m.m.m.c = 2⁴×3²×5=720
120=2³×5×3
48=3×2⁴
72=3²×2³