#### Answer

Doesn't make sense.

#### Work Step by Step

Their product must be $+72$, which is positive,
so both integers must be negative, or both positive.
Their sum is negative, so they both should be negative.
"All number pairs... " includes -3 and 20, 83 and -100, 983 and -1000 etc.
This would be a waste of time since none of the products of these pairs can be positive.
Instead of all number pairs, you could start by
searching pairs of NEGATIVE integers whose sum is -17.
In fact, the best start (the least time consuming start) you might have is to list the pairs of negative factors of +72.