What is an absolute value? what does it do? when would we need to use an absolute value

Absolute Value Absolute Value means ...

... only how far a number is from zero:

"6" is 6 away from zero,
and "−6" is also 6 away from zero. So the absolute value of 6 is 6,
and the absolute value of −6 is also 6

More Examples:

The absolute value of −9 is 9The absolute value of 3 is 3The absolute value of 0 is 0The absolute value of −156 is 156 No Negatives!

So in practice "absolute value" means to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).

Absolute Value Symbol

To show that we want the absolute value of something, we put "|" marks either side (they are called "bars" and are found on the right side of a keyboard), like these examples:

|−5| = 5 |7| = 7 Sometimes absolute value is also written as "abs()", so abs(−1) = 1 is the same as |−1| = 1

Absolute Value is the magnitude of a real number without regard to its sign, in other words Absolute value makes everything inside of it positive. The absolute value is used in the real world to define the DIFFERENCE or change from one point to another. A good example I found was that if the everybody is going 55 mph and you are going 70  or 40 mph you will most likely get a ticket.  It matters because the difference between you and everybody else is 15 mph.  Not -15 or +15 but 15. Absolute value plays it's part into the equation because you don't need it to be +15 or -15 but plain 15.
Hope This Helps!

31 is prime. and it’s prime factorization is just 31.

Ireally don’t understand your problem do you have a better picture of it