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

To find the greatest common factor (GCF) of the numbers \(16 n^{4}\), \(12 n^{4}\), \(8 n^{4}\), and \(14 n^{4}\), we first identify the GCF of the coefficients (16, 12, 8, and 14) and then include the variable part. 1. The coefficients are: - 16 factors into \(2^4\) - 12 factors into \(2^2 \times 3\) - 8 factors into \(2^3\) - 14 factors into \(2^1 \times 7\) 2. The GCF of the coefficients: - The common factor among these coefficients is \(2^1\), since that is the smallest exponent of 2 among them. 3. The variable part: - All terms have \(n^4\), so we take \(n^4\). Combining these, we find that the GCF is: \[ 2 n^{4} \] Thus, the greatest common factor is \(2 n^{4}\).