In the problem, when 144 is divided by n it leaves a remainder of 11. This is the same when 220 is divided by n. So the first step would be to subtract the remainder of 11 from both numbers. This leaves us with 133 and 209 and n divides into both with 0 remainders. Now to find n, we have to find the highest common factor, as both numbers have the same factor of n. By breaking down both numbers into their factors, we find that the highest common factor between both numbers is 19. To check if 19 is indeed n, we can simply divide 133 or 209 by 19 on a calculator and if there are 0 remainders then 19 must be n. Alternatively, we can divide 144 or 220 by 19 in our heads, or on paper, and if there is a remainder of 11 then 19 is n.
144/n = remainder of 11
220/n = remainder of 11
144 - 11 = 133
220 - 11 = 209
HCF of 133 and 209 = 19
n = 19