List all the pairs of integers with a product of 36. then find the pair whose sum is 20

This is an excellent practice for the solution of quadratic equations.

1*36=36 = > (1,36)

2*18=36 = > (2,18)

3*12=36 = > (3,12)

4*9=36 = > (4,9)

6*6=36 = > (6,6)

9*4=36 = > (9,4)

12*3=36 = > (12,3)

18*2=36 = > (18,2)

36*1=36 = > (36,1)

We can see that the sum decreases until the two factors are close (or equal) and then increases again.

The pair of integers with a sum of 20 is therefore (2,18) or (18,2).