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What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1,2 and 3 respectively?

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364

626

422

456

answer is D.

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Detailed Solution

The given integers are 626, 3127 and 15628.
Subtract the remainders 1, 2 and 3 from 626, 3127 and 15628. That is,

626 - 1 = 625

3127 - 2 = 3125

15628 - 3 = 15625

The HCF of 625, 3125, and 15625 is calculated as follows:

15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5

3125 = 5 \times 5 \times 5 \times 5 \times 5

625 = 5 \times 5 \times 5 \times 5

HCF = 5 \times 5 \times 5 \times 5

\Rightarrow HCF = 325

Therefore, 625 is the largest number that divides 626, 3127, and 15628 and leave remainders of 1, 2 and 3 respectively.
Hence, option 4 is correct.

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