Question

determinati numerele naturale a si b, stiind ca: (a,b) = 12 si a•b = 2160

Answer 1

a=12x;b=12y;a*b=2160=> 12x*12y=2160=> x*y=2160:144=>x*y=15. produsul a doua nr trebuie sa fie 15. exista situatiile 1 ) x=1=>a=12 si y=15=>b=180; 2)x=3=>a=36 si y=5=>b=60; 3) x=5=>a=60 si y=3=>b=36; 4) x=15=>a=180 si y=1=>b=12