Find Greatest Common Divisor of 123456789 and 987654321, using Euclidean algorithm.
Answer
The GCD of given numbers is 9.
Explanation
Step 1 :
Divide $ 987654321 $ by $ 123456789 $ and get the remainder
The remainder is positive ($ 9 > 0 $), so we will continue with division.
Step 2 :
Divide $ 123456789 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 9 }} $.
We can summarize an algorithm into a following table.
| 987654321 | : | 123456789 | = | 8 | remainder ( 9 ) | ||
| 123456789 | : | 9 | = | 13717421 | remainder ( 0 ) | ||
| GCD = 9 | |||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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