To solve the question in the image: "What is the prime factorization of 1,008?" let's break down 1,008 into its prime factors step by step.

Step-by-Step Prime Factorization of 1,008:

1. Start by dividing 1,008 by 2, the smallest prime number, because 1,008 is even: $1,008 \div 2 = 504$
2. Continue dividing by 2: $504 \div 2 = 252$ $252 \div 2 = 126$ $126 \div 2 = 63$
3. Now, 63 is not divisible by 2, so move to the next prime number, 3: $63 \div 3 = 21$ $21 \div 3 = 7$
4. Finally, 7 is a prime number, so the process stops here.

Thus, the prime factorization of 1,008 is: $1,008 = 2^4 \times 3^2 \times 7$

Now, looking at the answer choices in the image, the correct option would be:

• $7 \times 2^4 \times 3^2$

Do you have any other questions, or would you like more details about this factorization process?

Here are some follow-up questions to expand on this concept:

1. How do you determine if a number is divisible by a prime?
2. What are the benefits of prime factorization in solving larger problems?
3. Can you factor other numbers similarly? For example, factorize 360.
4. How can you verify your factorization is correct?
5. What other number properties can be deduced from its prime factorization?

Tip: Always start dividing by the smallest prime (2) and continue with larger primes like 3, 5, 7, etc.