1. Stating the problem: We need to find the largest common factor (also called greatest common divisor, GCD) of each pair of numbers. 2. Formula and rules: The largest common factor of two numbers is the greatest number that divides both without leaving a remainder. 3. Method: To find the GCD, we can use the Euclidean algorithm which involves repeated division and taking remainders until the remainder is zero. 4. Example: Suppose the pair is (a, b). We perform the steps: $$\text{GCD}(a,b) = \text{GCD}(b, a \bmod b)$$ Repeat until remainder is zero. 5. Explanation: This works because the GCD of two numbers also divides their difference. 6. Intermediate work: For example, if the pair is (48, 18): $$48 \div 18 = 2 \text{ remainder } 12$$ $$\text{GCD}(48,18) = \text{GCD}(18,12)$$ $$18 \div 12 = 1 \text{ remainder } 6$$ $$\text{GCD}(18,12) = \text{GCD}(12,6)$$ $$12 \div 6 = 2 \text{ remainder } 0$$ $$\text{GCD}(12,6) = 6$$ 7. Final answer: The largest common factor of 48 and 18 is 6. This method applies to any pair of numbers to find their largest common factor.