Find the greatest common factor. $$ 16 n^{4}, 12 n^{4}, 8 n^{4}, 14 n^{4} $$

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1. Write the coefficients of the terms:
   - $$16$$
   - $$12$$
   - $$8$$
   - $$14$$

2. Factor each coefficient into primes:
   - $$16 = 2^4$$
   - $$12 = 2^2 	imes 3$$
   - $$8 = 2^3$$
   - $$14 = 2 	imes 7$$

3. Identify the common prime factors:
   - All coefficients have a factor of $$2$$.

4. Determine the smallest exponent of $$2$$ across the coefficients:
   - The exponents of $$2$$ are $$4$$, $$2$$, $$3$$, and $$1$$. The smallest is $$1$$, so the common factor from the numbers is $$2^1 = 2$$.

5. Include the common variable factor:
   - Each term contains $$n^4$$.

6. Combine the results:
   - The greatest common factor is $$2n^4$$.
The greatest common factor is $$2n^{4}$$.

Find the greatest common factor.

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