Question
Find Greatest Common Divisor of 816 and 1071, using Euclidean algorithm.
Answer
The GCD of given numbers is 51.
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.
| 1071 | : | 816 | = | 1 | remainder ( 255 ) | ||||
| 816 | : | 255 | = | 3 | remainder ( 51 ) | ||||
| 255 | : | 51 | = | 5 | remainder ( 0 ) | ||||
| GCD = 51 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
816
1071
3
17
2
2
2
2
3
7
The GCD equals the product of the numbers at the intersection.
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