Find Greatest Common Divisor of 99 and 101, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 101 $ by $ 99 $ and get the remainder
The remainder is positive ($ 2 > 0 $), so we will continue with division.
Step 2 :
Divide $ 99 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2 $ 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.
| 101 | : | 99 | = | 1 | remainder ( 2 ) | ||||
| 99 | : | 2 | = | 49 | remainder ( 1 ) | ||||
| 2 | : | 1 | = | 2 | 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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