111

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#003333" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Álgebra de Baldor"><U><B>Algebra de Baldor</B></U></A><B> |  </B><A HREF="id1076.htm" TARGET="_top" TITLE="Índice temático"><U><B>Índice temático</B></U></A><B>  |  </B><A HREF="id1073.htm" TARGET="_top" TITLE="Lista"><U><B>Lista de Ejercicios</B></U></A><B> |</B></div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>111</B></div> <div> <B>M á x i m o   c o m ú n   d i v i s o r</B></div> <div> <B>Máximo común divisor de monomios</B></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <div>       <FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" > </FONT></div> <DIV ALIGN="LEFT"></DIV> <div> <B>P r o c e d i m i e n t o </B></div> <bR> <div> <B>P</B>ara hallar el máximo común divisor de dos o mas monomios se procede como sigue:</div> <bR> <div> <B>1.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >  Se halla el m.c.d. (máximo común divisor) de los coeficientes numericos:</FONT></div> <div> <B>a.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >  Se descomponen los números en sus factores primos</FONT></div> <div> <B>b.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >  Se multiplican los factores primos comunes y con el menor exponente</FONT></div> <div> <FONT SIZE="4" COLOR="#FF9999" FACE="Times New Roman" ><B>c.</B></FONT>  Para representar el m.c.d., <I>k</I>,  de los números <I>a</I> y <I>b</I>, se utiliza la simbología <FONT SIZE="4" COLOR="#0099FF" FACE="Times New Roman" >(<I>a</I>, <I>b</I>) = <I>k</I></FONT></div> <div> <B>2.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >  A continuación del m.c.d. de los coeficientes numéricos se escriben las letras comunes y, con el menor exponente</FONT></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Enunciados y enlaces a las soluciones de los problemas del Ejercicio 111</B></div> <bR> <div> <B>          S</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >olución en imagen <IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> y o video <IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> de los catorce problemas del Ejercicio 111:</FONT></div> <div> <B>H</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >allar el m.c.d. de:</FONT></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="803d61190.gif" border=0 width="97" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#1" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="803e75190.gif" border=0 width="117" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#2" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="803f741b0.gif" border=0 width="116" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#3" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="80408b190.gif" border=0 width="139" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#4" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/tPPH5KaxdRU" TARGET="_top" TITLE="https://youtu.be/tPPH5KaxdRU"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="804198190.gif" border=0 width="152" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#5" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/i570UysnSiQ" TARGET="_top" TITLE="https://youtu.be/i570UysnSiQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="8042ab190.gif" border=0 width="171" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#6" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/FJdsYRTPQhw" TARGET="_top" TITLE="https://youtu.be/FJdsYRTPQhw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="8043e3190.gif" border=0 width="227" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#7" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/rwRztnXTH5k" TARGET="_top" TITLE="https://youtu.be/rwRztnXTH5k"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="8044ec1b0.gif" border=0 width="236" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/kA-dA5H2adM" TARGET="_top" TITLE="https://youtu.be/kA-dA5H2adM"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="#8" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="804507190.gif" border=0 width="263" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/4UGzN_9358U" TARGET="_top" TITLE="https://youtu.be/4UGzN_9358U"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="#9" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >        <IMG SRC="8046211b0.gif" border=0 width="289" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/K-CPA2Oy-ps" TARGET="_top" TITLE="https://youtu.be/K-CPA2Oy-ps"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="#10" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >       </FONT></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="8047081b0.gif" border=0 width="264" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/SsVHjW5mFbA" TARGET="_top" TITLE="https://youtu.be/SsVHjW5mFbA"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="#11" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="8048291b0.gif" border=0 width="297" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/VCnyna_uFhk" TARGET="_top" TITLE="https://youtu.be/VCnyna_uFhk"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="#12" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >      </FONT></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="8049fc190.gif" border=0 width="252" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/VjUwI2jj0iw" TARGET="_top" TITLE="https://youtu.be/VjUwI2jj0iw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="#13" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >        <IMG SRC="804a071b0.gif" border=0 width="263" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/AKknGl8QOWQ" TARGET="_top" TITLE="https://youtu.be/AKknGl8QOWQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="#14" TITLE="111"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Soluciones de los problemas del Ejercicio 111</B></div> <bR> <div> <B>H</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >allar el m.c.d. de:</FONT></div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <IMG SRC="5eedc5a70.gif" border=0 width="709" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <IMG SRC="5eeeaca70.gif" border=0 width="684" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <IMG SRC="5eefa9a70.gif" border=0 width="681" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <IMG SRC="5ef065a70.gif" border=0 width="869" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <IMG SRC="5d7269a70.gif" border=0 width="873" height="167" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="5ef174a70.gif" border=0 width="884" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>7</div> <div> <IMG SRC="5ef2b7a70.gif" border=0 width="951" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>8</div> <div> <IMG SRC="5ef3b7a70.gif" border=0 width="951" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>9</div> <div> <IMG SRC="5ef4bca70.gif" border=0 width="956" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>10</div> <div> <IMG SRC="5d73d8c50.gif" border=0 width="984" height="197" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>11</div> <div> <IMG SRC="5ef5c5a70.gif" border=0 width="965" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>12</div> <div> <IMG SRC="5ef6d1a70.gif" border=0 width="977" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>13</div> <div> <IMG SRC="5ef785a70.gif" border=0 width="645" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="14"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>14</div> <div> <IMG SRC="5d74a8a70.gif" border=0 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