# Find the highest common factor of 432 and 522

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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.

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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