质因数分解

Question 1

您可以尝试以下方法：

$$
  \begin{array}{|l}
    \llap{2~~~~} 12600 \\ \hline
    \llap{2~~~~} 6300  \\ \hline
    \llap{2~~~~} 3150  \\ \hline
    \llap{5~~~~} 1575  \\ \hline
    \llap{5~~~~} 315   \\ \hline
    \llap{7~~~~} 63    \\ \hline
    \llap{3~~~~} 9     \\ \hline
                 3
  \end{array}
$$

以下是渲染的输出数学：

Answer

您可以尝试以下方法：

$$
  \begin{array}{|l}
    \llap{2~~~~} 12600 \\ \hline
    \llap{2~~~~} 6300  \\ \hline
    \llap{2~~~~} 3150  \\ \hline
    \llap{5~~~~} 1575  \\ \hline
    \llap{5~~~~} 315   \\ \hline
    \llap{7~~~~} 63    \\ \hline
    \llap{3~~~~} 9     \\ \hline
                 3
  \end{array}
$$

以下是渲染的输出数学：

Question 2

这里我创建了\mydiv来实际进行计算，如果您提供连续的素因数。语法是\mydiv[<dividend>]{<divisor>}。如果<dividend>省略，则使用先前计算的被除数。

该宏会检测因式分解何时完成。

如果您实际输入了非因素，则会出现错误。

如果 Mathjax 不允许访问stackengine，我已经提供了简化的代码来代替它......

\documentclass{article}
\def\rlwd{.5pt} \def\rlht{\dimexpr\dp\strutbox+\ht\strutbox} \def\rldp{.75ex}
\newcommand\mydiv[2][\relax]{\noindent%
  \if\relax#1\relax%
    \xdef\theremainder{\the\numexpr\dividend - %
      \numexpr\numexpr\dividend/\divisor\relax*\divisor\relax\relax}%
    \xdef\dividend{\the\numexpr\dividend/\divisor\relax}%
  \else%
    \xdef\dividend{#1}%
    \xdef\theremainder{0}%
  \fi%
  \xdef\divisor{#2}%
  \ifnum\dividend=\divisor\finishmydiv\checkfactor\else%
  \makebox[3ex][r]{#2}~\setbox0=\hbox{~$\dividend$}%
  \dumbstackengine{-\rlwd}{\rule[-\rldp]{\rlwd}{\rlht}~\dividend}{\rule{\dimexpr4pt+\wd0}{\rlwd}}%
\checkfactor%
\\%
  \fi%
}
\def\finishmydiv{%
  \makebox[3ex][r]{}\hspace{\dimexpr1ex%
  }~\dividend\relax}
\def\checkfactor{\ifnum\theremainder=0\relax\else\ [Remainder${}=\theremainder$]\fi}
%%% \EITHER THIS (IF stackengine IS NOT AVAILABLE+)
%\makeatletter
%\global\newlength\@stackedboxwidth
%\newlength\@boxshift
%\newsavebox\@addedbox
%\newsavebox\@anchorbox
%\newcommand*\dumbstackengine[3]{%
%    \sbox{\@anchorbox}{$#2$}%
%    \sbox{\@addedbox}{$#3$}%
%    \setlength{\@stackedboxwidth}{\wd\@anchorbox}%
%      \ifdim\wd\@addedbox>\@stackedboxwidth%
%        \setlength{\@stackedboxwidth}{\wd\@addedbox}%
%      \fi%
%        \setlength{\@boxshift}{\dimexpr-\dp\@anchorbox -\ht\@addedbox -#1}%
%        \usebox{\@anchorbox}%
%        \hspace{-\wd\@anchorbox}%
%        \raisebox{\@boxshift}{\usebox{\@addedbox}}%
%        \hspace{-\wd\@addedbox}%
%        \hspace{\@stackedboxwidth}%
%}
%\makeatother
%%% OR
\usepackage{stackengine}
\newcommand*\dumbstackengine[3]{\stackengine{#1}{#2}{#3}{U}{l}{F}{F}{S}}
%%%
\begin{document}
\mydiv[12600]{2} 
\mydiv{2} 
\mydiv{2} 
\mydiv{5} 
\mydiv{5} 
\mydiv{7} 
\mydiv{3} 
\mydiv{3}\medskip

\mydiv[60]{3} 
\mydiv{3} 
\mydiv{5}
\mydiv{2}
\end{document}

大致基于我的回答如何输入短除法？

Answer