Two consecutive factors can be represented by x and x+1, so we can write 20<=x(x+1)<=90. We can write two quadratic equations: x(x+1)-20>=0 and x(x+1)-90<=0. That is, x^2+x-20>=0 and x^2+x-90<=0, which become:
(x-4)(x+5)>=0 and (x-9)(x+10)<=0, so 4<=x<=9
So the pairs are 4,5; 5,6; 6,7; 7,8; 8,9; 9,10.