1. **State the problem:** Find the greatest common factor (GCF) of the numbers 48 and 136. 2. **Prime factorization:** - Factor 48: $$48 = 2^4 \times 3$$ - Factor 136: $$136 = 2^3 \times 17$$ 3. **Identify common prime factors:** - Both have the prime factor 2. - The smallest power of 2 common to both is $$2^3$$. 4. **Calculate the GCF:** $$\text{GCF} = 2^3 = 8$$ 5. **Explanation:** The greatest common factor is the product of all prime factors common to both numbers, raised to the lowest power they appear in either number. **Final answer:** $$\boxed{8}$$