Ответ:

[tex]5[/tex]

Пошаговое объяснение:

[tex]{\begin{array}{l}{\begin{array}{r|r}25&5 \\ 5&5 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \phantom{8} \\ \phantom{8} \\ \end{array}} \\ \end{array}}&&{\begin{array}{l}{\begin{array}{r|l}40&2 \\ 20&2 \\ 10&2 \\ 5&5 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}&&{\begin{array}{l}{\begin{array}{r|l}100&2 \\ 50&2 \\ 25&5 \\ 5&5 \\ 1&\; \\ \end{array}} \\ {\begin{array}{l}\phantom{8} \\ \end{array}} \\ \end{array}}[/tex]

[tex]\\25=5\cdot 5=5^{2}\\40=2\cdot 2\cdot 2\cdot 5=2^{3}\cdot 5\\100=2\cdot 2\cdot 5\cdot 5=2^{2}\cdot 5^{2}[/tex]

НCД(25,40,100)=5