Since
7 * 8 = 56
a good place to start could be
70 * 80 = 5,600
Then
72 * 80 = (70 + 2) * 80 = (70 * 80) + (2 * 80)
= 5,600 + 160 = 5,760
This number is larger than 5,590, so let's pick another factor smaller than 80 by subtracting away as many 72s as we need:
5,760 - 72 = 5,688 = 72 * 79
5,688 - 72 = 5,616 = 72 * 78
5,616 - 72 = 5,544 = 72 * 77
So the quotient is 77, and we have
5,590 = (72 * 77) + 46