Question
Find Greatest Common Divisor of 2364 and 78, using Euclidean algorithm.
Answer
The GCD of given numbers is 6.
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.
| 2364 | : | 78 | = | 30 | remainder ( 24 ) | ||||
| 78 | : | 24 | = | 3 | remainder ( 6 ) | ||||
| 24 | : | 6 | = | 4 | remainder ( 0 ) | ||||
| GCD = 6 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
2364
78
2
3
2
197
13
The GCD equals the product of the numbers at the intersection.
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