To do this, we first need to calculate the prime factorisations of 432 and 522, that is to say we need to break the numbers down into their prime factors.Let's start with 432. 432 = 2 x 216432 = 2 x ( 2 x 108)432 = 2 x 2 x (2 x 54)432 = 2 x 2 x 2 x (9x6)432 = 2 x 2 x 2 x (3 x 3) x (2 x 3)Therefore, the prime factorisation of 432 is 24 x 33SImilarly with 522,522 = 2 x 261522 = 2 x (3 x 87)522 = 2 x 3 x (3 x 29)Since 29 is a prime number, the prime factorisation of 522 is 2 x 32 x 29.Now, to calculate the highest common factor of the two numbers, we can draw a Venn diagram to find the intersection of the two factorisations. For now, imagine it like this. 432 BOTH 52223 3 2 32 29Therefore, the intersection of the two factorisations is 2 and 32, which means that the highest common factor is just those numbers multiplied.So the HCF of 432 and 522 = 2 x 32 = 18