Find Greatest Common Divisor of 77 and 110, using Euclidean algorithm.
Answer
The GCD of given numbers is 11.
Explanation
Step 1 :
Divide $ 110 $ by $ 77 $ and get the remainder
The remainder is positive ($ 33 > 0 $), so we will continue with division.
Step 2 :
Divide $ 77 $ by $ \color{blue}{ 33 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 3 :
Divide $ 33 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.
We can summarize an algorithm into a following table.
| 110 | : | 77 | = | 1 | remainder ( 33 ) | ||||
| 77 | : | 33 | = | 2 | remainder ( 11 ) | ||||
| 33 | : | 11 | = | 3 | remainder ( 0 ) | ||||
| GCD = 11 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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