document.write( "Question 1162454: What is the greatest integer, which when divided into 383, 527, or 815 leaves the same remainder? \n" ); document.write( "

Algebra.Com's Answer #786263 by ikleyn(52942) $\"\"$ $\"About$

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document.write( "Let N be that number.\r\n" );
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document.write( "Then 383 divided by N, 527 divided by N and 815 divided by N give the same remainder.\r\n" );
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document.write( "It implies that the difference  527 - 383 = 144  is divisible by N\r\n" );
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document.write( "            and the difference  815 - 527 = 288  is divisible by N.\r\n" );
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document.write( "So, presumably N = 144, and we must check it.\r\n" );
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document.write( "    383 divided by 144 gives the remainder 95.\r\n" );
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document.write( "    527 divided by 144 gives the remainder 95.\r\n" );
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document.write( "    815 divided by 144 gives the remainder 95.\r\n" );
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document.write( "ANSWER.  The number under the question is 144.\r\n" );
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