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If N is the greatest number that divides 2238, 4474 and 7828, leaving same remainder in each case, then what is the product of the digits of N?

If N is the greatest number that divides 2238, 4474 and 7828, leaving same remainder in each case, then what is the product of the digits of N? Correct Answer 8

The largest number which divides a, b and c to leave same remainder in each case = HCF (a-b, b-c, c-a). The greatest number that divides 2238, 4474 and 7828, leaving same remainder in each case = HCF (4474-2238, 7828-4474, 7828-2238) = HCF (2236, 3354, 5590) = 1118. Therefore, product of the digits of 1118 = 1*1*1*8 = 8.

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