154954

Firstly, I thought about what the equation actually means. We are told that 144/n gives a remainder of 11 and that 220/n also gives a remainder of 11. The remainder of 11 means that 11 is left over after the division, therefore I subtracted 11 away from 144 and 220 to find the multiples of n. 144-11= 133 and 220-11=209. After this, I found the common factors using a factor tree. The factors of 133 are 1,7,19,133 and the factors of 209 are 1,11,19,209. We can see from this that they both share a common factor, 19. From the equations we have done, we now know some facts about the number 19, it is a factor of 133 and 209 and if you add the remainder of 11 it confers with the numbers first given to us, 144 and 220. That is how I solved this question.