Factor this

We don't really need to list all the pairs . Let's calculate the total number of pairs first .

$A \times B = 360 = 2^3 \times 3^2 \times 5 .$

Total pairs = $(3+1)\times(2+1)\times(1+1) = 24$ . These are all the ordered pairs with positive integer $A$ and $B$ . Unordered pairs will be $\dfrac{24}{2} = 12$ . Out of these $12$ pairs $6$ of them will have $A < 6$ . Total Pairs left $= 6$ . Since negative integers are also included , total pairs are $\boxed{6 \times 2 =12}$

The pairs are:

$(8, 45), (-8, -45), (9, 40), (-9, -40), (10, 36), (-10, -36), (12, 30), (-12, -30), (15, 24), (-15, -24), (18, 20), (-18, -20)$

That's 12 pairs.