Discussion
The greatest number which can divide 1356, 1868 and 2764 having the same remainder 12 in each case is ______ ?
Answer: A
Subtract the common remainder: 1356 - 12 = 1344, 1868 - 12 = 1856 and 2764 - 12 = 2752. The greatest divisor is the HCF of these.
1856 - 1344 = 512, and the HCF of 1344 and 512 is 64, which also divides 2752 (2752 = 43 x 64). So the number is 64, option A.
A number that leaves remainder 12 in each case divides 1344, 1856 and 2752 exactly, and the greatest such number is their HCF, which is 64 (1344 = 21 x 64, 1856 = 29 x 64, 2752 = 43 x 64). The remainder 12 is less than 64, so the answer is valid.
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