1. **State the problem:** Find the prime factorization of 630. 2. **Recall the formula and rules:** Prime factorization means expressing a number as a product of prime numbers. 3. **Start dividing 630 by the smallest prime number 2:** $$630 \div 2 = 315$$ 4. **Next, divide 315 by the next smallest prime 3:** $$315 \div 3 = 105$$ 5. **Divide 105 by 3 again:** $$105 \div 3 = 35$$ 6. **Divide 35 by the next prime 5:** $$35 \div 5 = 7$$ 7. **Finally, 7 is a prime number itself.** 8. **Write the prime factorization:** $$630 = 2 \times 3 \times 3 \times 5 \times 7 = 2 \times 3^2 \times 5 \times 7$$ This means 630 is composed of the prime factors 2, 3 squared, 5, and 7.