Question
Find Greatest Common Divisor of 216 and 234, using Euclidean algorithm.
Answer
The GCD of given numbers is 18.
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 zero => GCD is the last divisor .
We can summarize an algorithm into a following table.
| 234 | : | 216 | = | 1 | remainder ( 18 ) | ||
| 216 | : | 18 | = | 12 | remainder ( 0 ) | ||
| GCD = 18 | |||||||
This solution can be visualized using a Venn diagram.
0,0
216
234
2
3
3
2
2
3
13
The GCD equals the product of the numbers at the intersection.
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