Question
Find Greatest Common Divisor of 30193 and 6831139, using Euclidean algorithm.
Answer
The GCD of given numbers is 109.
Explanation
Step 1 :
Divide by and get the remainder
The remainder is positive (), so we will continue with division.
Step 2 :
Divide by and get the remainder
The remainder is still positive (), so we will continue with division.
Step 3 :
Divide by and get the remainder
The remainder is zero => GCD is the last divisor .
We can summarize an algorithm into a following table.
| 6831139 | : | 30193 | = | 226 | remainder ( 7521 ) | ||||
| 30193 | : | 7521 | = | 4 | remainder ( 109 ) | ||||
| 7521 | : | 109 | = | 69 | remainder ( 0 ) | ||||
| GCD = 109 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
30193
6831139
109
277
7
7
1279
The GCD equals the product of the numbers at the intersection.
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