Find the prime factorization of the composite number. \[ 85,800 \] Choose the prime factorization of 85,800 . A. $2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13$ c. $2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 13$ E. $5^{2} \cdot 8 \cdot 11 \cdot 13$ G. $2 \cdot 3 \cdot 11 \cdot 13 \cdot 100$ B. $3 \cdot 8 \cdot 11 \cdot 13 \cdot 25$ D. $2^{3} \cdot 3 \cdot 11 \cdot 13 \cdot 25$ F. $2 \cdot 3 \cdot 5 \cdot 11 \cdot 13$ H. $2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13$

Step 1 ：To solve this problem, we need to find the prime factorization of the number 85,800. Prime factorization is the process of determining the prime numbers that multiply together to make a certain number. We can do this by dividing the number by prime numbers, starting from the smallest prime number (which is 2), and continuing until we can't divide anymore.

Step 2 ：The prime factors of 85800 are 2, 2, 2, 3, 5, 5, 11, 13. This corresponds to the prime factorization \(2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13\).

Step 3 ：Final Answer: The prime factorization of 85800 is \(\boxed{2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13}\).