1. **Problem:** A forester wants to plant 68 apple trees and 110 mango trees in equal rows (same number of trees per row). Each row contains only one type of tree. Find the minimum number of rows required. 2. **Formula and concept:** To plant trees in equal rows with only one type per row, the number of trees per row must be a divisor of both 68 and 110. The minimum number of rows corresponds to the greatest common divisor (GCD) of 68 and 110. 3. **Find the GCD:** - Prime factors of 68: $68 = 2^2 \times 17$ - Prime factors of 110: $110 = 2 \times 5 \times 11$ - Common prime factors: $2$ - So, $\gcd(68,110) = 2$ 4. **Calculate number of rows:** - Number of rows for apple trees: $\frac{68}{2} = 34$ - Number of rows for mango trees: $\frac{110}{2} = 55$ - Total minimum rows = $34 + 55 = 89$ **Final answer:** The minimum number of rows required is **89**.