document.write( "Question 550112: The natural number n is the smallest number satisfying the following properties: when divided by 3 remainder is 1,when divided by 4 remainder is 2,when divided by 5 remainder is 3,when divided by 6 remainder is 4,what is the remainder in case of division by 7? \n" ); document.write( "

Algebra.Com's Answer #358461 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The natural number n is the smallest number satisfying the following properties: when divided by 3 remainder is 1,
\n" ); document.write( "when divided by 4 remainder is 2,
\n" ); document.write( "when divided by 5 remainder is 3,
\n" ); document.write( "when divided by 6 remainder is 4,
\n" ); document.write( "what is the remainder in case of division by 7?
\n" ); document.write( ":
\n" ); document.write( "I can't think of an algebra equation that can solve this but we can use some logic here.
\n" ); document.write( "Since one of the requirements is divide by 5, remainder 3, we know the number has a unit value of 3 or 8
\n" ); document.write( "Also if it meets the requirement of divide by 6, remainder 4, it will automatically satisfy the requirement of divide 3, remainder 1
\n" ); document.write( "This narrows it down, I wrote numbers;
\n" ); document.write( "18, 23, 28, 33, 38, 43, 48, 53, 58, 63
\n" ); document.write( "easy to throw out 18, 28, 33, 48, 63
\n" ); document.write( "tried, 23, 38, 43, 53, then came the winner 58!!
\n" ); document.write( ":
\n" ); document.write( "\"what is the remainder in case of division by 7\"
\n" ); document.write( "58/7 = 8 remainder 2
\n" ); document.write( ":
\n" ); document.write( "I am thinking there may be a more efficient way to do this, but just can't come up with it this Christmas Eve. Merry Christmas!! \n" ); document.write( "

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