human
Task: Write a medium-length social media post based on the reading. Follow the **tone** but not the entire structure in the example.

Example: Do you know how to find the sum of all the factors of a number? 🤔 For example, the factors of 18 are 1, 2, 3, 6, 9 and 18. If you add them up, you get 39. 😊 But what if the number is really big, like 360? 😱 Don’t worry, there’s a formula for that! 💪

Here’s how it goes:

1. Write the number as a product of prime factors with exponents. (18 = 2^1 × 3^2)

2. Add up all the powers of each prime factor from zero to its exponent. (For 2 we have 2^0 + 2^1 = 1 + 2 = 3; For 3 we have 3^0 + 3^1 + 3^2 = 1 + 3 + 9 = 13)

3. Multiply the sums of each prime factor. (3 × 13 = 39)

So the sum of all the factors of 18 is 39! 🎉

But why does this formula work? We can imagine two boxes with balls that have numbers on them.

Box A contains powers of 2: 1 and 2. Box B contains powers of 3: 1, 3 and 9.

If we pick one ball from each box and multiply their numbers, we get a factor of 18. For example, if we pick the balls with numbers 2 and 3, we get 2 × 3 = 6. To find the sum of all the factors of 18, we need to add up all the possible products of the balls picked.

Sum of factors = (2^0 × 3^0) + (2^0 × 3^1) + (2^0 × 3^2) + (2^1 × 3^0) + (2^1 × 3^1) + (2^1 × 3^2)

Using the distributive property: 
Sum of factors = [2^0 × (3^0 + 3^1 + 3^2)] + [2^1 × (3^0 + 3^1 + 3^2)] 
= (2^0 + 2^1) × (3^0 + 3^1 + 3^2) 🙌

With this formula, you can easily find the sum of all the positive factors of 360! Write 
gpt
--- Reasoning ---
1. Is the question multiple-choice question?
No
2. Is it implied multiple-choice question?
No
3. If two experts were independently asked the question, will the final answer be exactly the same?
No

--- Answer ---
open