Answer :
The last non-zero remainder is the GCD of the two numbers. Since the remainder is now zero, we stop the process. Therefore, the GCD of 181 and 104 is 1.
To determine the greatest common divisor (GCD) of 181 and 104 using the Euclidean algorithm, follow these steps:
1. The Euclidean algorithm is a method used to find the GCD of two numbers by repeatedly dividing the larger number by the smaller number and replacing the larger number with the remainder until the remainder is zero. The last non-zero remainder is the GCD of the two numbers.
2. Start with the two given numbers, 181 and 104.
3. Divide 181 by 104. The quotient is 1 and the remainder is 77.
4. Replace 181 with 104 and 104 with the remainder, which is 77.
5. Divide 104 by 77. The quotient is 1 and the remainder is 27.
6. Replace 104 with 77 and 77 with the remainder, which is 27.
7. Divide 77 by 27. The quotient is 2 and the remainder is 23.
8. Replace 77 with 27 and 27 with the remainder, which is 23.
9. Divide 27 by 23. The quotient is 1 and the remainder is 4.
10. Replace 27 with 23 and 23 with the remainder, which is 4.
11. Divide 23 by 4. The quotient is 5 and the remainder is 3.
12. Replace 23 with 4 and 4 with the remainder, which is 3.
13. Divide 4 by 3. The quotient is 1 and the remainder is 1.
14. Replace 4 with 3 and 3 with the remainder, which is 1.
15. Divide 3 by 1. The quotient is 3 and the remainder is 0.
16. Since the remainder is now zero, we stop the process.
17. The last non-zero remainder is 1.
Conclusion:
Therefore, the GCD of 181 and 104 is 1.
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