Question
Calculate the difference between number of factors and sum
of factors of 396.Solution
Since, 396 = 2 2 Â X 3 2 Â 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)Â - 1)/(X - 1)] X [(Y (b + 1) Â - 1)/(Y - 1)] X [(Z (c + 1) Â - 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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