Explain in detail using the results of problem 2 how the fol

Explain in detail using the results of problem 2, how the following calculation gives that gcd(252, 198) = 18.

thanks in advance!

3. (a) Explain in detail using the results of problem 2, how the following calculation gives that gcd(252, 198) = 18. 252 = 1-198 + 54 198 3-54 + 36 54 = 1.36 + 18 36 = 2.18+0 (b) Let a and b be integers, with a 2 0. Explain how to obtain integers q and r with 0

Solution

Yo u are trying to find the GCD of 252 and 198
divide 252 by 198
quotient = 1
remainder = 54

now divide 198 by 54
quotient = 3
remainder = 36

now divide 54 by 36
quotient = 1
remainder = 18

you havw to repeat this process untill remainder = 0
now divide 36 by 18
quotient = 2
remainder = 0

once remainder is 0,
GCD = 18 (THE LAST DEVISOR)
Answer: 18

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b = qa+r
q is quotient when b is divided by a
r is remainder when b is divided by a
In this way you can get q and r