Find the greatest number that will divide 445,572 and 699 leaving remainder 4,5 and 6 respectively.

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answer is B.

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Detailed Solution

The given integers are 445,572 and 699.
Subtract the remainders 4, 5 and 6 from 445, 572, and 699. That is,

445 - 4 = 441

572 - 5 = 567

699 - 6 = 693

Calculation of the HCF of 441, 567, and 693 as follows:

693 = 3 \times 3 \times 7 \times 11

567 = 3 \times 3 \times 3 \times 3 \times 7

441 = 3 \times 3 \times 7 \times 7

HCF = 3 \times 3 \times 7

\Rightarrow HCF = 63

Therefore, 63 is the largest number that divides 445, 572, and 699 and leaves remainders of 4, 5 and 6 respectively.
Hence, option 2 is correct.

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