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    Question

    Find the largest number that, when dividing 259, 323,

    and 640, leaves remainders of 4, 8, and 10, respectively.
    A 25 Correct Answer Incorrect Answer
    B 19 Correct Answer Incorrect Answer
    C 17 Correct Answer Incorrect Answer
    D 15 Correct Answer Incorrect Answer

    Solution

    The required number will divide 255 (259 - 4) , 315 (323 - 8) and 630 (640 - 10) completely.

    Now, the greatest number that will divide 255, 315 and 630 completely, is the HCF of these numbers.

    255 = 3 X 5 X 17

    315 = 32 X 5 X 7

    630 = 2 x 32 x 5 x 7

    So, HCF of 255, 315 and 630 = 3 x 5 = 15

    Therefore, required number is 15.

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