1. The problem states: Determine if 12 is a common factor of 20 and 35. 2. A common factor of two numbers is a number that divides both numbers exactly without leaving a remainder. 3. To check if 12 is a common factor, we divide both 20 and 35 by 12 and check the remainders. 4. Calculate $20 \div 12 = 1$ remainder $8$ (since $20 - 12 \times 1 = 8$). 5. Calculate $35 \div 12 = 2$ remainder $11$ (since $35 - 12 \times 2 = 11$). 6. Since both divisions leave remainders (8 and 11), 12 does not divide either 20 or 35 exactly. 7. Therefore, 12 is not a common factor of 20 and 35. Final answer: 12 is not a common factor of 20 and 35.