Determine the greatest common factor of the following 4x2y2, 3xy4, 2xy2

Well we solve each of these individually.
For the first one 4x2y2 we will apply the exponent rule of a^b * a^c = a^b + c.
So...
2^2 * 4xy
4 * 4xy, apply the same exponent rule.
4^2xy > 16xy (GCF)

For 3xy4 it is very simple.
Simply multiply the numbers 3 * 4 = 12 or 12xy (GCF)

For 2xy2 apply the exponent rule we used before above.
2 * 2 = 2^1 + 1 = 2^2 > 2^2xy = 4xy(GCF)

Therefore we have 
4x2y2 = 16xy
3xy4 = 12xy
2xy2 = 4xy

Out of all of these, which has the greatest GCF? :)

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