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 #358527 by richard1234(7193) $\"\"$ $\"About$

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Here I use \"mod\" to shorten the solution. \"Mod\" or \"modulo\" is another way of expressing remainders.\r
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\n" ); document.write( "\n" ); document.write( "The number is 3 mod 5 so the units digit must be either 3 or 8. We also know the number is 2 mod 4, so it must be even but not divisible by 4. Hence the units digit is 8. Also, it is 1 mod 3 so 28, 58, 88, 118, ... are the choices. 58 is the smallest positive integer that works, and 58 is congruent to 2 mod 7, so the remainder is 2. \n" ); document.write( "

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