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Chapter 5: Problem 48

Find the greatest common divisor of the numbers. 66 and 90

Short Answer

Expert verified
The greatest common divisor of 66 and 90 is 6.

Step by step solution

01

Apply Euclidean Algorithm

By applying the Euclidean Algorithm, first divide the larger number by the smaller number. Calculate the remainder. In this case, divide 90 (larger number) by 66 (smaller number). 90 divided by 66 gives a quotient of 1 and the remainder is 24.
02

Continue the process

Now, replace the larger number by the smaller number and the smaller number by the remainder obtained. Continue this process until the remainder is zero. So, now divide 66 by 24 (remainder of previous step). 66 divided by 24 gives a quotient of 2 and the remainder is 18.
03

Repeat the step 2

Continuing like this, now divide 24 (previous divisor) by 18 (remainder of previous step). The result is a quotient of 1 and remainder is 6.
04

Proceed with Euclidean Algorithm

Continuing the process, now divide 18 (previous divisor) by 6 (remainder of previous step). The result is a quotient of 3 and the remainder is 0.
05

Identify GCD

Once the remainder is zero, the divisor at this stage will be the GCD of the original two numbers. So, the GCD of 66 and 90 is 6.

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