In section 1.1, we learned the division theorem, greatest common divisors, and Euclid's algorithm. These problems will help you practice.
1. If b = 10 and a = 6 use the division theorem to find the quotient q and the remainder.

2. If b = 20 and a = 6 use the division theorem to find the quotient q and the remainder.

3. If b = 34 and a = 13 use the division theorem to find the quotient q and the remainder.

4. The gcd(10, 12) =

5. The gcd(10, 13) =

6. The gcd(20, 40) =

7. The gcd(24, 24) =

8. The gcd(24, 8) =

9. The gcd(11571, 1767) =

10. Calculate gcd(10,31), and find a linear combination of the dividends that yields this gcd.
10* + 31* =

11. Calculate gcd(20,24), and find a linear combination of the dividends that yields this gcd.
20* + 24* =

12. Calculate gcd(40,96), and find a linear combination of the dividends that yields this gcd.
40* + 96* =

13. Calculate gcd(48,12), and find a linear combination of the dividends that yields this gcd.
48* + 12* =

14. Calculate gcd(12,24), and find a linear combination of the dividends that yields this gcd.
12* + 24* =

15. Calculate gcd(24,64), and find a linear combination of the dividends that yields this gcd.
24* + 64* =

16. Reduce the fraction 861 / 984 to lowest terms.
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17. Reduce the fraction 132 / 924 to lowest terms.
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18. Reduce the fraction 378 / 868 to lowest terms.
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