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(A) To find the greatest number $N$ that divides $a, b,$ and $c$ leaving the same remainder,we calculate the $HCF$ of the differences of the numbers:

Vedclass · Accepted Answer

$4$

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(A) To find the greatest number $N$ that divides $a, b,$ and $c$ leaving the same remainder,we calculate the $HCF$ of the differences of the numbers: $(b-a), (c-b),$ and $(c-a)$.Here,$a = 1305, b = 4665, c = 6905$.Differences are:$4665 - 1305 = 3360$$6905 - 4665 = 2240$$6905 - 1305 = 5600$Now,find the $HCF$ of $3360, 2240,$ and $5600$.$3360 = 1120 	imes 3$$2240 = 1120 	imes 2$$5600 = 1120 	imes 5$Thus,$N = HCF(3360, 2240, 5600) = 1120$.The sum of the digits of $N = 1 + 1 + 2 + 0 = 4$.

Let $N$ be the greatest number that will divide $1305, 4665,$ and $6905,$ leaving the same remainder in each case. Then the sum of the digits in $N$ is:

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