Question

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

Answer 1

The common factors with integer coefficients are:

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

Explanation:

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`