Factor is the numbers that divides another number or expression without the remainder. For example, 3 and 6 are factors of 12 because 12÷ 3=4 and 12÷6=2.
The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.
1.

We want to find
such that
. This means



so
is conservative.
2.

Then




so
is conservative.
3.

so
is not conservative.
4.

Then




so
is conservative.