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    The smallest prime number that is a divisor of 17408 is 2 (17408 = 17 × 2102^{10}210​). What is the sum of digits of the greatest prime number, which
    Question

    The smallest prime number that is a divisor of 17408 is 2 (17408 = 17 × 2102^{10}​). What is the sum of digits of the greatest prime number, which is a divisor of 17391?

    A.

    4

    B.

    5

    C.

    8

    D.

    6

    Correct option is A

    Given:

    17408 = 17×21017 \times 2^{10}

    Solution:

    17391 = 17408 - 17

    17×2101717 \times 2^{10} - 17​​

    =  17(2101)17(2^{10} - 1)​​

    = 17(1024 - 1)

    17×102317 \times 1023​​

    17×3×11×3117 \times 3 \times 11 \times 31​​

    Thus, the greatest prime number = 31.

    Sum of digits = (3 + 1) = 4

    Thus, the correct option is (a) 4

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