Discussion

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Answer: A

The required number is the HCF of the differences between the given numbers.

Differences are: \((91 - 43) = 48\), \((183 - 91) = 92\), and \((183 - 43) = 140\).

We need to find the HCF of 48, 92, and 140.

Prime factorization of 48 = \(2^4 \times 3\).

Prime factorization of 92 = \(2^2 \times 23\).

Prime factorization of 140 = \(2^2 \times 5 \times 7\).

The highest common factor is \(2^2 = 4\).

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