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Find the highest common factor of 432 and 522

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 216

432 = 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 33

SImilarly with 522,

522 = 2 x 261

522 = 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                        522

23   3                         2       32                        29

Therefore, 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

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