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    Question

    Calculate the difference between number of factors and sum

    of factors of 396.
    A 1074 Correct Answer Incorrect Answer
    B 1286 Correct Answer Incorrect Answer
    C 1054 Correct Answer Incorrect Answer
    D 1284 Correct Answer Incorrect Answer

    Solution

    Since, 396 = 2 2  X 3 2  X 11

    So, number of factors = (2 + 1) X (2 + 1) X (1 + 1) = 3 X 3 X 2 = 18

    If number is written as X a   X Y b  X Z c , then its sum of factors (N) is given as:

    N = [(X (a + 1)  - 1)/(X - 1)] X [(Y (b + 1)  - 1)/(Y - 1)] X [(Z (c + 1)  - 1)/(Z - 1)]

    Sum of factors = [(2 (2 + 1)  - 1)/(2 - 1)] X [(3 (2 + 1)  - 1)/(3 - 1)] X [(11 (1 + 1)  – 1)/(11 - 1)] = 7 X 13 X 12 = 1092

    Required difference = 1092 - 18 = 1074

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