document.write( "Question 1184385: M is a whole number whose units digit is a 4. When the 4 is moved from the units digit to the left side of the number, a new number, p is formed. P is equal to 4 x M and has the same digits as M. What is the smallest possible value of M? \n" ); document.write( "

Algebra.Com's Answer #814950 by Edwin McCravy(20067) $\"\"$ $\"About$

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document.write( "Let the whole number with the digit 4 removed be N.\r\n" );
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document.write( "Then the whole number = 10N+4\r\n" );
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document.write( "4 times this whole number = 4(10N+4) = 40N+16\r\n" );
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document.write( "This must equal to p = N + 4*10^a, where a is some integer. So\r\n" );
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document.write( "The right side is 40000000...0, but we don't know what \"a\" is so\r\n" );
document.write( "we don't know where the 0's stop.\r\n" );
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document.write( "However we do know that \r\n" );
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document.write( "dividend = quotient*divisor + remainder\r\n" );
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document.write( " 4*10^a  =        N*39      +    16\r\n" );
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document.write( "40000... =        N*39      +    16\r\n" );
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document.write( "So we start dividing 39 into 40000000... and if we ever get a remainder\r\n" );
document.write( "of 16, we will have our answer for N  So let's see if we can get a 16\r\n" );
document.write( "remainder:\r\n" );
document.write( "             10256      \r\n" );
document.write( "         39)400000000000...\r\n" );
document.write( "            39\r\n" );
document.write( "             10\r\n" );
document.write( "             00\r\n" );
document.write( "             100\r\n" );
document.write( "              78\r\n" );
document.write( "              220\r\n" );
document.write( "              195\r\n" );
document.write( "               250\r\n" );
document.write( "               234\r\n" );
document.write( "                16    <--aha! we got a remainder of 16.\r\n" );
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document.write( "So N, the number without the 4 on the right end is 10256\r\n" );
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document.write( "So M = 102564 and p = 4M = 410256\r\n" );
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document.write( "Edwin

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