Question

Exercitiul 19 va rog, cu rezolvare pas cu pas, mulțumesc​

Answer 1

 

$\displaystyle\bf\\n=numarul~cautat\\\\1558:n=c_1~rest~58\\~~526:n=c_2~rest~26\\1043:n=c_3~rest~43\\\\(1558-58):n=c_1\\(526-26):n=c_2\\(1043-43):n=c_3\\\\(1558-58)=1500\\(526-26)=500\\(1043-43)=1000\\\\n=cmmdc~al~numerelor~(1500;~500;~1000)\\\\Descompunem~numerele:\\\\1500=15\times10^2=3\times5\times2^2\times5^2=2^2\times3\times5^3\\500=5\times10^2=5\times2^2\times5^2~~~~~~~~~=2^2\times5^3\\1000=10^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=2^3\times5^3\\\\cmmdc=2^2\times5^3\\\boxed{\bf n=500}$