Question

Знайдіть НСД чисел:
1) 250 і 75; 2) 134 і 86; 3) 13 і 133; 4) 280 і 216.

Answer 1

Ответ:

1) 25

2) 2

3) 1

4) 8

Объяснение:

$1)\\{\begin{array}{l}{\begin{array}{r|r}250&2 \\ 125&5 \\ 25&5 \\ 5&5 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}&&{\begin{array}{l}{\begin{array}{r|l}75&3 \\ 25&5 \\ 5&5 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8} \\ \end{array}} \\ \end{array}}\\\\250=2\cdot 5\cdot 5\cdot 5=2\cdot5^{3}\\75=3\cdot 5\cdot 5=3\cdot5^{2}$

НCД(250,75)=5²=25

$2)\\{\begin{array}{l}{\begin{array}{r|r}134&2 \\ 67&67 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}&{\begin{array}{l}{\begin{array}{r|l}86&2 \\ 43&43 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}\\\\134=2\cdot 67\\ 86=2\cdot 43$

НCД(134,86)=2

$3)\\ {\begin{array}{l}{\begin{array}{r|r}13&13 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8} \\ \end{array}} \\ \end{array}}&{\begin{array}{l}{\begin{array}{r|l}133&7 \\ 19&19 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}\\\\13=13\\133=7\cdot 19$

НCД(13,133)=1

$4)\\{\begin{array}{l}{\begin{array}{r|r}280&2 \\ 140&2 \\ 70&2 \\ 35&5 \\ 7&7 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8} \\ \end{array}} \\ \end{array}}&&{\begin{array}{l}{\begin{array}{r|l}216&2 \\ 108&2 \\ 54&2 \\ 27&3 \\ 9&3 \\ 3&3 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}\\\\280=2\cdot 2\cdot 2\cdot 5\cdot 7=2^{3}\cdot 5\cdot7\\216=2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 3=2^{3}\cdot3^{3}$

НCД(280,216)=2³=8