Question

Знайти НСД чисел: 1) 25, 75, 425 2) 34, 374, 238

Answer 1

Ответ:

1) НCД(25,75,425)=25

2) НCД(34,374,238)=34

Пошаговое объяснение:

1)

${\begin{array}{l}{\begin{array}{r|r}25&5 \\ 5&5 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8} \\ \end{array}} \\ \end{array}}&&{\begin{array}{l}{\begin{array}{r|l}75&3 \\ 25&5 \\ 5&5 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}&&{\begin{array}{l}{\begin{array}{r|l}425&5 \\ 85&5 \\ 17&17 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}$

$25=5\cdot 5=5^{2}\\75=3\cdot 5\cdot 5=3 \cdot 5^{2}\\425=5\cdot 5\cdot 17=5^{2}\cdot17$

НCД(25,75,425)=5²=25

2)

${\begin{array}{l}{\begin{array}{r|r}34&2 \\ 17&17 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8} \\ \end{array}} \\ \end{array}}&&{\begin{array}{l}{\begin{array}{r|l}374&2 \\ 187&11 \\ 17&17 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}&&{\begin{array}{l}{\begin{array}{r|l}238&2 \\ 119&7 \\ 17&17 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}$

$34=2\cdot 17\\374=2\cdot 11\cdot 17\\238=2\cdot 7\cdot 17$

НCД(34,374,238)=2⋅17=34

Answer 2

1) Чтобы найти НСД чисел 25, 75 и 425, можно использовать алгоритм Евкли