Calculate the difference between number of factors and sum

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