<P>장재영 선생님의 답글입니다.</P> <P> </P> <DIV class=board> <P>문제 : 100! 를 6진법으로 계산하면 끝자리 연속하는 0의 개수는?</P> <P> </P> <P>풀이 : 어떤 수를 6진법의 수로 나타낼때 끝자리 연속하는 0의 개수가 n개일 필요충분조건은 그 수가 인수로서 6 을 n개 가져야한다(6진법의 전개식에서 생각하면 됨).</P> <P> </P> <P> <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=179 align=absMiddle height=18><PARAM NAME="_cx" VALUE="4736"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/42`4.3/12,[1]{100!`equal`100`times`99`times` `hdot3` `times`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이고 </P> <P>100= <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=273 align=absMiddle height=18><PARAM NAME="_cx" VALUE="7223"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/63`4.3/12,[1]{2`times`50, 50`equal`2`times`25, 25`equal`2`times`12`plus`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> , <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=77 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2037"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/17.8`4.3/12,[1]{12`equal`2`times`6}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>, <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=176 align=absMiddle height=18><PARAM NAME="_cx" VALUE="4656"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/39.9`4.3/12,[1]{6`equal`2`times`3, 3`equal`2`times`1`plus`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>이므로 100!은 소인수로서 2를 97(=50+25+12+6+3+1)개 가진다. </P> <P>한편 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=120 align=absMiddle height=18><PARAM NAME="_cx" VALUE="3175"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/27.9`4.3/12,[1]{100`equal`3`times`33`plus`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>이고 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=85 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2248"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/19.8`4.3/12,[1]{33`equal`3`times`11}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>, <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=104 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2751"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/23.9`4.3/12,[1]{11`equal`3`times`3`plus`2}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>, <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=69 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1825"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/15.8`4.3/12,[1]{3`equal`3`times`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이므로 100! 은 소인수로 3을 48(=33+11+3+1)개 가진다.</P> <P> </P> <P>따라서 100!은 인수로 6(= <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=40 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1058"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/9.4`4.3/12,[1]{2`times`3}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>)을 48개 갖는다. </P> <P>따라서 답은 48개.</P></DIV>
