Well something for example.Would be if you were a contactor,you need to find measurements of lots of things. For example that could be needing to find the sum of 2 sides.And find the sum of the 2 sides of that right trainagle can determine if the biulding has a good foundation . And thats how you can use a Pythagorean Theorem in the real world !
Yes you just have to cross multiply
Assuming that you meant factor family to be a factor tree.
32 8 4
16 2 4 2 2 2
4 4 2 2
2 2 2 2