document.write( "Question 889114: what is the digit in the unit place (593)^143 \n" ); document.write( "
Algebra.Com's Answer #537903 by Edwin McCravy(20060)\"\" \"About 
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document.write( "The units digit is the last digit.\r\n" );
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document.write( "If we multiply any number ending in 3 by a number ending in 3,\r\n" );
document.write( "we get a number ending in 9, since 3x3=9\r\n" );
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document.write( "If we then multiply that number ending in 9 by a number ending \r\n" );
document.write( "in 3, we get a number ending in 7, since 9x3=27\r\n" );
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document.write( "If we then multiply that number ending in 7 by a number ending \r\n" );
document.write( "in 3, we get a number ending in 1, since 7x3=21\r\n" );
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document.write( "If we then multiply that number ending in 1 by a number ending \r\n" );
document.write( "in 3, we get a number ending in 3, since 1x3=3.\r\n" );
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document.write( "Then the pattern starts all over again.\r\n" );
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document.write( "So if we continue t0 multipy 593x593x593x593x..., we continue\r\n" );
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document.write( "to get the pattern of last digits 3,9,7,1,3,9,7,1,....  So we \r\n" );
document.write( "just need to divide 143 by 4 to see how many times the cycle \r\n" );
document.write( "of last digits 3,9,7,1,3,9,7,1,... we go through in multiplying \r\n" );
document.write( "a number ending in 3 by itself.\r\n" );
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document.write( "   35\r\n" );
document.write( "4)143\r\n" );
document.write( "  12\r\n" );
document.write( "   23\r\n" );
document.write( "   20\r\n" );
document.write( "    3\r\n" );
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document.write( "So the quotient 35 tells us that the last digits would cycle\r\n" );
document.write( "around through the pattern 3,9,7,1, 35 times and the 3 remainder \r\n" );
document.write( "tells us that it would ends with a 7, since 7 is the third member \r\n" );
document.write( "of the cycle 3,9,7,1.\r\n" );
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document.write( "Answer: 7\r\n" );
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document.write( "Edwin
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