Question

Numerele 47,53,64 impartite la acelasi numar natural nenul n dau resturile 2, 3 si respectiv 4.Determinati numarul natural n.

Answer 1

47:n=c1 rest 2
47=n*c1+2
n*c1=47-2=45

53:n=c2 rest 3
53=n*c2+3
n*c2=53-3=50

64:n=c3 rest4
64=n*c3+4
n*c3=64-4=60

=>n=(45;50;60)
n-cel mai mare

45=3² *5
50=5² *2
60=2²*3*15

(45;50;60)=5  ⇒n=5