Find the greatest common factor, GCF, for the group of expressions. \[ 6(r+t)^{4}, 15(r+t)^{6} \] The GCF of the given expression is $\square$.

Step 1 ：Given the expressions are $6(r+t)^{4}$ and $15(r+t)^{6}$.

Step 2 ：We are looking for the greatest common factor (GCF) of these expressions.

Step 3 ：First, we find the GCF of the coefficients 6 and 15. The prime factors of 6 are 2 and 3, and the prime factors of 15 are 3 and 5. The common prime factor is 3.

Step 4 ：Next, we find the GCF of the variables $(r+t)^{4}$ and $(r+t)^{6}$. The common factor is $(r+t)^{4}$ because it is the smallest power.

Step 5 ：So, the GCF of the given expressions is the product of the common prime factor and the common variable factor, which is $3(r+t)^{4}$.

Step 6 ：\(\boxed{3(r+t)^{4}}\) is the greatest common factor of the given expressions.