Final answer:
To find the greatest common factor of 10y^3 and 7c^4, identify the prime factors of each term and take the product of the common factors with the lowest exponent.
Step-by-step explanation:
To find the greatest common factor of 10y^3 and 7c^4, we need to identify the common factors of the two terms.
The prime factors of 10y^3 are 2, 5, and y, while the prime factors of 7c^4 are 7 and c.
The greatest common factor is the product of the common prime factors raised to the lowest exponent, which in this case is 1 for all the common factors.
Therefore, the greatest common factor of 10y^3 and 7c^4 is 1.