Find Greatest Common Divisor of 101 and 126, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 126 $ by $ 101 $ and get the remainder
The remainder is positive ($ 25 > 0 $), so we will continue with division.
Step 2 :
Divide $ 101 $ by $ \color{blue}{ 25 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 3 :
Divide $ 25 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
| 126 | : | 101 | = | 1 | remainder ( 25 ) | ||||
| 101 | : | 25 | = | 4 | remainder ( 1 ) | ||||
| 25 | : | 1 | = | 25 | remainder ( 0 ) | ||||
| GCD = 1 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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