1. The problem is to find the greatest common divisor (GCD) of 10932 and 3150. 2. We use the Euclidean algorithm, which involves repeated division and taking remainders. 3. Compute $10932 \div 3150$ which gives quotient 3 and remainder $10932 - 3 \times 3150 = 10932 - 9450 = 1482$. 4. Now find GCD(3150, 1482). 5. Compute $3150 \div 1482$ which gives quotient 2 and remainder $3150 - 2 \times 1482 = 3150 - 2964 = 186$. 6. Now find GCD(1482, 186). 7. Compute $1482 \div 186$ which gives quotient 7 and remainder $1482 - 7 \times 186 = 1482 - 1302 = 180$. 8. Now find GCD(186, 180). 9. Compute $186 \div 180$ which gives quotient 1 and remainder $186 - 1 \times 180 = 6$. 10. Now find GCD(180, 6). 11. Compute $180 \div 6$ which gives quotient 30 and remainder 0. 12. When remainder is 0, the GCD is the divisor at this step, which is 6. Therefore, the greatest common divisor of 10932 and 3150 is $6$.