1. **State the problem:** Find the (a) Greatest Common Factor (GCF) and (b) Least Common Multiple (LCM) of 16 and 72. 2. **Recall definitions:** - The GCF of two numbers is the largest number that divides both without a remainder. - The LCM of two numbers is the smallest number that is a multiple of both. 3. **Find prime factorizations:** - $16 = 2^4$ - $72 = 2^3 \times 3^2$ 4. **Find GCF:** - Take the minimum powers of common primes. - Common prime is 2. - Minimum power of 2 is $3$. - So, $\text{GCF} = 2^3 = 8$ 5. **Find LCM:** - Take the maximum powers of all primes present. - For 2: max power is 4. - For 3: max power is 2. - So, $\text{LCM} = 2^4 \times 3^2 = 16 \times 9 = 144$ **Final answers:** - (a) GCF = 8 - (b) LCM = 144