Question

aflati cel mai mare divizor comun al nr naturale a si b stiind ca a×b=180 [a,b]=60 a×b =1890,[a,b]=630 a×b=1000[a,b]=100​

Answer 1

a=60p

b=60r unde psi r∈N

cu (p;r)=1 pt ca cmmdc=60 si nu exista alt factor prim comun

aplicam formula

ab=(a,b)*[a,b]

 atunci

ab=60*1800= 1800*60=60p*60r=3600pr

1800*60=3600pr

simplific (impart fiecare  termen) prin 60

1800=60pr

mai simplific o data prin 60

30=pr

cum (p;r)=1⇒p=1 si r=30 sau

sau p=5 si r=6

sau =2 sir=15

deci a=60*1 =60 si b=60*30=1800

sau a=60*2=120 si b=60*15 =900

sau a=60*5=300 si b=60*6=360

si ,desigur, simetriceler lor

(1800;60); (900;120) si (360;300)