1. **Problem:** Find the prime factorization of 48 and 60 using exponents, then find the greatest common factor (GCF). 2. Prime factorization of 48: $$48 = 2 \times 24 = 2 \times 2 \times 12 = 2^3 \times 6 = 2^4 \times 3 = 2^4 \times 3^1$$ 3. Prime factorization of 60: $$60 = 2 \times 30 = 2^2 \times 15 = 2^2 \times 3 \times 5 = 2^2 \times 3^1 \times 5^1$$ 4. Find GCF by taking the minimum power of each common prime factor: $$\text{GCF} = 2^{\min(4,2)} \times 3^{\min(1,1)} = 2^2 \times 3^1 = 4 \times 3 = 12$$ 5. **Problem:** Find the prime factorization of 84 and 126 using exponents, then find the GCF. 6. Prime factorization of 84: $$84 = 2 \times 42 = 2^2 \times 21 = 2^2 \times 3 \times 7 = 2^2 \times 3^1 \times 7^1$$ 7. Prime factorization of 126: $$126 = 2 \times 63 = 2^1 \times 3^2 \times 7^1$$ 8. Find GCF by taking the minimum power of each common prime factor: $$\text{GCF} = 2^{\min(2,1)} \times 3^{\min(1,2)} \times 7^{\min(1,1)} = 2^1 \times 3^1 \times 7^1 = 42$$ 9. **Problem:** Find the prime factorization of 150 and 210 using exponents, then find the GCF. 10. Prime factorization of 150: $$150 = 2 \times 75 = 2^1 \times 3 \times 25 = 2^1 \times 3^1 \times 5^2$$ 11. Prime factorization of 210: $$210 = 2 \times 105 = 2^1 \times 3 \times 35 = 2^1 \times 3^1 \times 5 \times 7 = 2^1 \times 3^1 \times 5^1 \times 7^1$$ 12. Find GCF by taking the minimum power of each common prime factor: $$\text{GCF} = 2^{\min(1,1)} \times 3^{\min(1,1)} \times 5^{\min(2,1)} = 2^1 \times 3^1 \times 5^1 = 30$$ 13. **Problem:** Find the prime factorization of 64 and 96 using exponents, then find the GCF. 14. Prime factorization of 64: $$64 = 2^6$$ 15. Prime factorization of 96: $$96 = 2^5 \times 3^1$$ 16. Find GCF by taking the minimum power of each common prime factor: $$\text{GCF} = 2^{\min(6,5)} = 2^5 = 32$$ **Final answers:** - For 48 and 60, GCF = 12 - For 84 and 126, GCF = 42 - For 150 and 210, GCF = 30 - For 64 and 96, GCF = 32