Find Greatest Common Divisor of 78 and 66, using Euclidean algorithm.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 :
Divide $ 78 $ by $ 66 $ and get the remainder
The remainder is positive ($ 12 > 0 $), so we will continue with division.
Step 2 :
Divide $ 66 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 3 :
Divide $ 12 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.
We can summarize an algorithm into a following table.
| 78 | : | 66 | = | 1 | remainder ( 12 ) | ||||
| 66 | : | 12 | = | 5 | remainder ( 6 ) | ||||
| 12 | : | 6 | = | 2 | remainder ( 0 ) | ||||
| GCD = 6 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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