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Sum of all factors of a number

A small number, like 24, has few factors, which can be added together easily to get the sum:
1 + 2 + 2 + 2 + 3 + 24 = 34
So the sum of all factors of 24 is 34.

But large numbers have a lot of factors. It is difficult to manually list and add all of them. For example, 8800 has 36 factors. How can you find the sum of all factors of a number without manually adding them? By applying some radical mathematical thinking, we will derive an easier way to get the sum of all factors of a number, without adding them manually.

Step 1: Prime factor the number 8800


Step 2: List all the prime factors

`8800 = 2 * 2 * 2 * 2 * 2 * 2 * 5 * 5 * 11`

Step 3: Write the factors in exponent notation

There are six 2's, two 5's and one 11 in the above factors list. Thus, the factors in exponent notation are:
`8800 = 2^6 * 5^2 * 11`