The greatest number that divides 411, 684, an | vedclass

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(C) To find the greatest number that divides $411, 684,$ and $821$ leaving remainders $3, 4,$ and $5$ respectively,we first subtract the remainders fr

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$136$

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(C) To find the greatest number that divides $411, 684,$ and $821$ leaving remainders $3, 4,$ and $5$ respectively,we first subtract the remainders from the respective numbers:$411 - 3 = 408$$684 - 4 = 680$$821 - 5 = 816$Now,we need to find the $H.C.F.$ of $408, 680,$ and $816$.First,find the $H.C.F.$ of $408$ and $680$:$680 = 408 	imes 1 + 272$$408 = 272 	imes 1 + 136$$272 = 136 	imes 2 + 0$So,the $H.C.F.$ of $408$ and $680$ is $136$.Next,find the $H.C.F.$ of $136$ and $816$:$816 = 136 	imes 6 + 0$Since $136$ divides $816$ completely,the $H.C.F.$ of $408, 680,$ and $816$ is $136$.Therefore,the required number is $136$.

The greatest number that divides $411, 684,$ and $821$ and leaves $3, 4,$ and $5$ as remainders,respectively,is

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