1. Let's start by stating the problem: You want to understand the prime factorization method. 2. Prime factorization is the process of expressing a number as a product of its prime factors. 3. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. 4. The method involves dividing the number by the smallest prime number possible and continuing to divide the quotient by prime numbers until the quotient is 1. 5. For example, to find the prime factors of 60: - Start with the smallest prime, 2. Since 60 is divisible by 2, divide: $$60 \div 2 = 30$$ - Divide 30 by 2 again: $$30 \div 2 = 15$$ - 15 is not divisible by 2, move to the next prime, 3: $$15 \div 3 = 5$$ - 5 is a prime number, so we stop here. 6. So, the prime factorization of 60 is: $$2 \times 2 \times 3 \times 5$$ or $$2^2 \times 3 \times 5$$. 7. This method helps break down numbers into their building blocks, which is useful in many areas of math like finding the greatest common divisor or least common multiple. 8. Remember, always start dividing by the smallest prime and continue until the quotient is 1. This is the prime factorization method explained step-by-step.