1. **Problem Statement:** We have 72 technicians and 96 network engineers. We want to arrange them in equal rows such that each row contains only technicians or only network engineers. We need to find the greatest number of workers that can be in each row. 2. **Understanding the problem:** The number of workers in each row must be a divisor of both 72 and 96 because each row has the same number of workers and only one type of worker. 3. **Mathematical approach:** We need to find the greatest common divisor (GCD) of 72 and 96. 4. **Formula for GCD:** The GCD of two numbers can be found using the Euclidean algorithm: $$\gcd(a,b) = \gcd(b, a \bmod b)$$ 5. **Applying Euclidean algorithm:** - Calculate $96 \bmod 72 = 24$ - Then $\gcd(72, 96) = \gcd(72, 24)$ - Calculate $72 \bmod 24 = 0$ - So $\gcd(72, 24) = 24$ 6. **Interpretation:** The greatest number of workers in each row is 24. **Final answer:** $$\boxed{24}$$ workers can be in each row.