Finding sum of factors of a number using prime factorization Given a number, there is an algorithm described here to find it's sum and number of factors.
For example, let us take the number $1225$ :

It's factors are $1, 5, 7, 25, 35, 49, 175, 245, 1225 $
and the sum of factors are $1767$.

A simple algorithm that is described to find the sum of the factors is using prime factorization.

$1225 = 5^2 \cdot 7^2$, therefore the sum of factors is $ (1+5+25)(1+7+49)  = 1767$

But this logic does not work for the number $2450$. Please check if it's working for $2450$

Edit :
Sorry it works for $2450$. I made some mistake in calculation.
Your approach works fine: $2450=2\cdot 5^2\cdot 7^2$, therefore the sum of divisor is $$(1+2)(1+5+25)(1+7+49)=5301=3\cdot 1767.$$ 

You are looking for the Formula For Sum Of Divisors, from there:


  Each of these sums is a geometric series; hence we may use the formula for sum of a geometric series to conclude 
  $$
\sum_{d|n}d = \prod_{i=1}^k \frac{p_i^{m_i+1}-1}{p_i-1}
$$
Sum of factors of  $2450$

The Factors are $2, 5^2, 7^2$.

Sum of the factors $= ( 2^0 + 2^1 ) × ( 5^0 + 5^1+  5^2)×( 7^0 + 7^1+ 7^2)
= 5301$