1. **State the problem:** Scarlett has 44 m of blue ribbon and 110 m of red ribbon. She wants to cut all the ribbon into smaller pieces of the same length with no ribbon left over. We need to find the longest possible length of each smaller piece. 2. **Understand the problem:** The length of each piece must be a divisor of both 44 and 110, so that when the ribbons are cut into pieces of that length, there is no leftover ribbon. 3. **Find the greatest common divisor (GCD):** The longest length that divides both 44 and 110 exactly is the GCD of 44 and 110. 4. **Calculate the GCD:** - Prime factorization of 44: $$44 = 2^2 \times 11$$ - Prime factorization of 110: $$110 = 2 \times 5 \times 11$$ - Common prime factors: 2 and 11 - Take the lowest powers: $$2^1 \times 11^1 = 2 \times 11 = 22$$ 5. **Conclusion:** The longest length Scarlett can make each smaller piece of ribbon is **22 meters**. **Final answer:** $$\boxed{22}$$ meters