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(D) To find the largest number that divides $2053$ and $967$ leaving remainders $5$ and $7$ respectively,we first subtract the remainders from the giv

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$64$

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(D) To find the largest number that divides $2053$ and $967$ leaving remainders $5$ and $7$ respectively,we first subtract the remainders from the given numbers.$2053 - 5 = 2048$$967 - 7 = 960$Now,we need to find the Highest Common Factor $(HCF)$ of $2048$ and $960$.Using the prime factorization method:$2048 = 2^{11}$$960 = 2^6 	imes 3 	imes 5$The $HCF$ is the product of the lowest powers of common prime factors:$HCF = 2^6 = 64$Therefore,the largest number is $64$.

Find the largest number that divides $2053$ and $967$ and leaves a remainder of $5$ and $7$ respectively.

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