To solve by prime factorization, you can follow these steps for various types of problems:

Example Problem:

Let's say we want to find the prime factorization of 180.

Steps to solve by prime factorizing:

1. Divide by smallest prime: Start with the smallest prime number, 2, and divide 180 by 2. $180 ÷ 2 = 90$
2. Continue dividing by 2: Divide 90 by 2 again. $90 ÷ 2 = 45$
3. Next smallest prime (3): 45 is not divisible by 2 anymore, so we move to the next smallest prime, 3. $45 ÷ 3 = 15$
4. Continue dividing by 3: Divide 15 by 3 again. $15 ÷ 3 = 5$
5. Final division (5): 5 is a prime number, so we stop here.

Thus, the prime factorization of 180 is: $180 = 2^2 × 3^2 × 5$

Would you like more details or have any questions on this?

Related Questions:

1. What is the prime factorization of 360?
2. How can we use prime factorization to find the greatest common divisor (GCD)?
3. How is prime factorization applied in finding the least common multiple (LCM)?
4. Why are prime factorizations unique for each number (Fundamental Theorem of Arithmetic)?
5. How can we use prime factorization to simplify fractions?

Tip: Always check the smallest primes first when factorizing, as it simplifies the process.