What are the common factors of 18xy and 32xy?

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Answer 1 · 2016-12-08T08:32:58

The common factors with integer coefficients are:

$+-1, +-2, +-x, +-2x, +-y, +-2y, +-xy, +-2xy$

The prime factorisations of $18$ and $32$ are:

$18 = 2*3^2$

$32 = 2^5$

Hence their common positive integer factors are:

$1, 2$

If you include negative integer factors then they have common factors:

$+-1, +-2$

Both $18xy$ and $32xy$ are multiples of $x$ and $y$ , so ignoring scalar multipliers, their common polynomial factors are:

$1, x, y, xy$

Putting all of the possible combinations together, all of their polynomial factors with integer coefficients are:

$+-1, +-2, +-x, +-2x, +-y, +-2y, +-xy, +-2xy$

The greatest common factor of $18xy$ and $32xy$ is $2xy$