Найдите все простые делители чисел:
- \({\largeа)}\ 4,\ 9,\ 15,\ 10,\ 24;\)
- \({\largeб)}\ 46,\ 50,\ 58,\ 99,\ 128;\)
- \({\largeв)}\ 196,\ 254,\ 400,\ 625,\ 10\ 000;\)
- \({\largeг)}\ 7,\ 77,\ 777,\ 7777,\ 77\ 777.\)
Задание 54
Источник заимствования: Алгебра. 7 класс. Учебник для общеобразовательных организаций / С.М. Никольский, М.К. Потапов, Н.Н. Решетников, А.В. Шевкин – Просвещение, 2013. – 13 c. ISBN 978-5-09-027739-6
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Решение:
- \({\largeа)}\ 4=2\cdot2=2^2\)
\(\phantom{\largeа)}\ \begin{array}[t]{ r|l}4&2\\2&2\\1\end{array}\) - \(\phantom{\largeа)}\ 9=3\cdot3=3^2\)
\(\phantom{\largeа)}\ \begin{array}[t]{ r|l}9&3\\3&3\\1\end{array}\) - \(\phantom{\largeа)}\ 15=3\cdot5\)
\(\phantom{\largeа)}\ \begin{array}[t]{ r|l}15&3\\5&5\\1\end{array}\) - \(\phantom{\largeа)}\ 10=2\cdot5\)
\(\phantom{\largeа)}\ \begin{array}[t]{ r|l}10&2\\5&5\\1\end{array}\) - \(\phantom{\largeа)}\ 24=2\cdot2\cdot2\cdot3=2^3\cdot3\)
\(\phantom{\largeа)}\ \begin{array}[t]{ r|l}24&2\\12&2\\6&2\\3&3\\1\end{array}\)
- \({\largeб)}\ 46=2\cdot23\)
\(\phantom{\largeб)}\ \begin{array}[t]{ r|l}46&2\\23&23\\1\end{array}\) - \(\phantom{\largeб)}\ 50=2\cdot5\cdot5=2\cdot5^2\)
\(\phantom{\largeб)}\ \begin{array}[t]{ r|l}50&2\\25&5\\5&5\\1\end{array}\) - \(\phantom{\largeб)}\ 58=2\cdot29\)
\(\phantom{\largeб)}\ \begin{array}[t]{ r|l}58&2\\29&29\\1\end{array}\) - \(\phantom{\largeб)}\ 99=3\cdot3\cdot11=3^2\cdot11\)
\(\phantom{\largeб)}\ \begin{array}[t]{ r|l}99&3\\33&3\\11&11\\1\end{array}\) - \(\phantom{\largeб)}\ 128=2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2=2^7\)
\(\phantom{\largeб)}\ \begin{array}[t]{ r|l}128&2\\64&2\\32&2\\16&2\\8&2\\4&2\\2&2\\1\end{array}\)
- \({\largeв)}\ 196=2\cdot2\cdot7\cdot7=2^2\cdot7^2\)
\(\phantom{\largeв)}\ \begin{array}[t]{ r|l}196&2\\98&2\\49&7\\7&7\\1\end{array}\) - \(\phantom{\largeв)}\ 254=2\cdot127\)
\(\phantom{\largeв)}\ \begin{array}[t]{ r|l}254&2\\127&127\\1\end{array}\) - \(\phantom{\largeв)}\ 400=2\cdot2\cdot2\cdot2\cdot5\cdot5=2^4\cdot5^2\)
\(\phantom{\largeв)}\ \begin{array}[t]{ r|l}400&2\\200&2\\100&2\\50&2\\25&5\\5&5\\1\end{array}\) - \(\phantom{\largeв)}\ 625=5\cdot5\cdot5\cdot5=5^4\)
\(\phantom{\largeв)}\ \begin{array}[t]{ r|l}625&5\\125&5\\25&5\\5&5\\1\end{array}\) - \(\phantom{\largeв)}\ 10\ 000=2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot5=2^4\cdot5^4\)
\(\phantom{\largeв)}\ \begin{array}[t]{ r|l}10\ 000&2\\5000&2\\2500&2\\1250&2\\625&5\\125&5\\25&5\\5&5\\1\end{array}\)
- \({\largeг)}\ 7=7\)
\(\phantom{\largeг)}\ \begin{array}[t]{ r|l}7&7\\1\end{array}\) - \(\phantom{\largeг)}\ 77=7\cdot11\)
\(\phantom{\largeг)}\ \begin{array}[t]{ r|l}77&7\\11&11\\1\end{array}\) - \(\phantom{\largeг)}\ 777=3\cdot7\cdot37\)
\(\phantom{\largeг)}\ \begin{array}[t]{ r|l}777&3\\259&7\\37&37\\1\end{array}\) - \(\phantom{\largeг)}\ 7777=7\cdot11\cdot101\)
\(\phantom{\largeг)}\ \begin{array}[t]{ r|l}7777&7\\1111&11\\101&101\\1\end{array}\) - \(\phantom{\largeг)}\ 77\ 777=7\cdot41\cdot271\)
\(\phantom{\largeг)}\ \begin{array}[t]{ r|l}77\ 777&7\\11\ 111&41\\271&271\\1\end{array}\)