Question

Scrieți numerele naturale de forma 2a3b diviziile cu 45

Answer 1

Răspuns:

2430; 2835

Explicație pas cu pas:

$\overline{2a3b} = 2000+100a+30+b = 2030 + 100a+b=\\\\ 2030:45 = 45\text{ rest }5\\100:45 = 2\text{ rest }10\\ \\ = (45\cdot 45+5)+ (2\cdot 45+10)a + b = \\ \\ = 45\cdot 45 + 2\cdot 45a + 10a+b+5= \\ \\ = 45\cdot(45+2a)+10a+b+5\\ \\ 10a+b+5\,\,\vdots\,\, 45 \Rightarrow (a,b) = \Big\{(4,0);\,\,(8,5)\Big\}\\ \\ \text{Verificare: }\\10\cdot 4+0+5 = 45\quad (A)\\ 10\cdot 8+5+5 = 90\quad (A)\\ \\ \Rightarrow 2a3b= \Big\{2430;\,2835\Big\}$