1. **State the problem:** We need to find the greatest number of students that can be arranged in each row such that each row contains only girls or only boys, and the number of students in each row is the same. 2. **Identify the numbers involved:** There are 48 girls and 64 boys. 3. **Understand the problem:** We want to find the greatest number that divides both 48 and 64 exactly. This is the Greatest Common Divisor (GCD) of 48 and 64. 4. **Recall the formula:** The GCD of two numbers is the largest positive integer that divides both numbers without leaving a remainder. 5. **Find the prime factors:** - 48 = $2^4 \times 3$ - 64 = $2^6$ 6. **Find the common prime factors with the smallest powers:** - Common prime factor is 2. - Smallest power of 2 in both is $2^4$. 7. **Calculate the GCD:** $$\text{GCD}(48,64) = 2^4 = 16$$ 8. **Interpretation:** The greatest number of students that could be in each row, with only girls or only boys, is 16. **Final answer:** 16