document.write( "Question 1182542: Find the last non-zero digit of 50! \n" ); document.write( "
Algebra.Com's Answer #812624 by math_tutor2020(3817)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "Check out this page \n" ); document.write( "https://math.stackexchange.com/questions/950502/how-to-find-the-last-non-zero-digit-of-50 \n" ); document.write( "The solution by Edward Jiang is probably the most straight forward process (that doesn't involve any complicated notation or concepts). That solution is the second provided on that page.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Recall that the exclamation marks indicate factorial \n" ); document.write( "Eg: 5! = 5*4*3*2*1 \n" ); document.write( "We can use the rule that \n" ); document.write( "(b!)/(a!) = b*(b-1)*...*(b-a+1)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So for example, if a = 10 and b = 20, then \n" ); document.write( "(b!)/(a!) = b*(b-1)*...*(b-a+1) \n" ); document.write( "(20!)/(10!) = 20*(20-1)*...*(20-10+1) \n" ); document.write( "(20!)/(10!) = 20*19*...12*11 \n" ); document.write( "(20!)/(10!) = 11*12*...*19*20 \n" ); document.write( "Note how we start with 11 (the value just after 10) counting our way up to 20, multiplying along the way.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "We could rephrase things as such \n" ); document.write( "(20!)/(10!) = (20*19*...*12*11*10!)/(10!) \n" ); document.write( "(20!)/(10!) = 20*19*...12*11 \n" ); document.write( "(20!)/(10!) = 11*12*...*19*20 \n" ); document.write( "In the second step, the \"10!\" terms cancel out.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "We would also say \n" ); document.write( "(30!)/(20!) = 21*22*...*29*30 \n" ); document.write( "(40!)/(30!) = 31*32*...*39*40 \n" ); document.write( "(50!)/(40!) = 41*42*...*49*50\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Hopefully this is enough to get you pointed in the right direction. \n" ); document.write( " \n" ); document.write( " |