Find the sum of all the factors of the number 55440.

Prime factorization of 55440.

$$55440=2^4\times3^2\times5\times7\times11$$

We know that the total factors will be equal to (4+1)*(2+1)*(1+1)*(1+1)*(1+1) = 120

And, the total number of even factors is equal to (3+1)*(2+1)*(1+1)*(1+1)*(1+1) = 96

To find the sum of all factors, we will put all the possible powers of any prime number and add them together and multiply with other primes.

$$2^4\times3^2\times5\times7\times11$$

Sum = $$\left(2^0+2^1+2^2+2^3+2^4\right)\times\left(3^0+3^1+3^2\right)\times\left(5^0+5^1\right)\times\left(7^0+7^1\right)\times\left(11^0+11^1\right)$$

=> 31*13*6*8*12

=> 232128