1. **State the problem:** Scarlett has 44 m of blue ribbon and 110 m of red ribbon. She wants to cut both ribbons 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. **Formula and concept:** To find the longest length that divides both 44 and 110 exactly, we need to find the Greatest Common Divisor (GCD) of 44 and 110. 3. **Find the GCD:** - Prime factors of 44: $2 \times 2 \times 11$ - Prime factors of 110: $2 \times 5 \times 11$ 4. **Common factors:** Both have $2$ and $11$ in common. 5. **Calculate GCD:** $$\text{GCD} = 2 \times 11 = 22$$ 6. **Interpretation:** The longest length for each smaller piece of ribbon is 22 meters. **Final answer:** The longest piece length is **22 meters**.