In how many different ways can 700 be expressed as the product of two positive integers? Show how you arrived at your answer.

There are 4,851 different ways that 700 can be expressed as the product of two positive integers.

Here's how you'd show your work for that problem:

***don't worry about the order of the two numbers when you first start, this is a common mistake***

Start with the equation C(99,2)

This in turn equals the following equation:

= (99)(98)/2

When you work that out, you get 4851. So the result is 4851 different ways that 700 (or any other number) can be expressed as the product of two positive integers.

We had 99 choices for the first number, and only 98 for the second (because the two integers couldn't be the same).

The order of the numbers doesn't matter - they don't have to be consecutive or anything, so I just divided by 2 to finally find the number of possible sets.