1. The problem is to express the number 300 as a product of its prime factors. 2. Start by dividing 300 by the smallest prime number 2: $$300 \div 2 = 150$$. 3. Divide 150 by 2 again: $$150 \div 2 = 75$$. 4. 75 is not divisible by 2, so move to the next prime number 3: $$75 \div 3 = 25$$. 5. 25 is not divisible by 3, so move to the next prime number 5: $$25 \div 5 = 5$$. 6. Divide 5 by 5: $$5 \div 5 = 1$$. 7. Since the quotient is 1, the prime factorization is complete. 8. Collecting all prime factors, we have: $$300 = 2 \times 2 \times 3 \times 5 \times 5 = 2^{2} \times 3 \times 5^{2}$$. 9. This is the prime factorization of 300.