Short Answer 
The process of finding the prime factorization of 675 begins by recognizing that 5 is a factor of 675, as it divides evenly. The prime factorization breakdown reveals that 675 can be expressed as 3^3 x 5^2, confirming its prime components.
Step 1: Identify the Division
The first step is to conduct the division of the numbers involved. In this case, we see that dividing 5 by 5 results in 1 with no remainder. This indicates that 5 is indeed a factor of the number we are analyzing, which is 675.
Step 2: Recognize Prime Factors
Next, we need to determine the prime factors of 675. Prime factors are the numbers that can be multiplied together to reach the original number and only consist of prime numbers. For 675, the key prime factors are:
- 3 (appearing three times)
- 5 (appearing two times)
Step 3: Construct the Factorization
The final step is to compile the identified prime factors together to illustrate how they reconstruct the original number. For 675, the factorization is:
- 3 x 3 x 3 x 5 x 5 = 675
This factorization confirms that we accurately broke down 675 into its core components, demonstrating the relationship between its factors.