Final answer:
To find the greatest common factor of 35y⁴, 14y⁴, and 63y⁴, factor out the common variable y⁴ and then determine the GCF of the numbers, which in this case is 7. The overall GCF is therefore 7y⁴.
Step-by-step explanation:
The greatest common factor (GCF) of 35y⁴, 14y⁴, and 63y⁴ is found by first factoring out the common variables and then finding the GCF of the numerical coefficients. Since all terms have y⁴, factor this out first:
y⁴(35, 14, 63)
Now, find the GCF of the numbers 35, 14, and 63. The GCF is the largest number that divides all of them without leaving a remainder.
35 = 5 × 7
14 = 2 × 7
63 = 9 × 7
The common factor among the numerical coefficients is 7. So, the GCF of 35, 14, and 63 is 7. Putting it back with the variable we factored out gives us:
GCF = 7y⁴