Final answer:
The greatest common factor (GCF) of 18y^8x^4w^6 and 30y^7w^3 is 6y^7w^3, found by identifying the greatest common divisor of the coefficients and the highest exponent of each variable present in both terms.
Step-by-step explanation:
To find the greatest common factor (GCF) of two expressions, we need to find the highest exponent of each variable that is present in both terms and the highest factor for the coefficient that divides both numbers. We start by identifying the factors of the coefficients: 18 and 30. The GCF of 18 and 30 is 6.
Next, we look at the variables. The highest exponent for y that is present in both terms is y^7, since that's the lower exponent between y^8 and y^7. x is only present in the first expression, so it is not included in the GCF. For w, the highest exponent present in both is w^3.
Therefore, the GCF of 18y^8x^4w^6 and 30y^7w^3 is 6y^7w^3.