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Question

(A) Let the number be $N$ and the divisor be $D$. According to the division algorithm,$N = D 	imes q_1 + 241$,where $q_1$ is the quotient. This impli

Vedclass · Accepted Answer

$370$

Vedclass · Answer

(A) Let the number be $N$ and the divisor be $D$. According to the division algorithm,$N = D 	imes q_1 + 241$,where $q_1$ is the quotient. This implies $N > 241$,so $D > 241$. When $2N$ is divided by $D$,the remainder is $112$. So,$2N = D 	imes q_2 + 112$. Substituting $N$ from the first equation: $2(D 	imes q_1 + 241) = D 	imes q_2 + 112$. $2D 	imes q_1 + 482 = D 	imes q_2 + 112$. $482 - 112 = D 	imes q_2 - 2D 	imes q_1$. $370 = D(q_2 - 2q_1)$. This shows that $D$ must be a factor of $370$. Since $D > 241$,the only factor of $370$ greater than $241$ is $370$ itself. Therefore,the divisor is $370$.

$A$ number when divided by a certain divisor leaves a remainder of $241$. When twice the number is divided by the same divisor,the remainder is $112$. Find the divisor.

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