Final answer:
The greatest common factor (GCF) of 25c³ and 15n⁴ is 5n².
Step-by-step explanation:
To find the greatest common factor (GCF) of 25c³ and 15n⁴, we need to determine the largest value that can divide both terms evenly. Let's break down the monomials into their prime factors:
- 25c³ = 5 x 5 x c x c x c
- 15n⁴ = 3 x 5 x n x n x n x n
From the prime factorization, we can see that the common factors are 5 and n². Therefore, the GCF is 5n².