126
The prime factors of 144 are 2, 2, 2, 2, 3 and 3
To get a negative sum and a positive product we need to use an even amount of negative numbers.
-2 x -3 = 6
-2 x -2 x -(2 x 3) = +4 x -6 = -24
-24 + 6 = -18
-144
268
That sounds like two different questions. The factors for -144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 and their negatives. The prime factors are 2 and 3. -16 and 9 add up to -7.
23
-134
-10 & -18
360
91
5298
The distinct prime factors of 550 are 2, 5 and 11. They add up to 18.
23
-273