Question
Find Greatest Common Divisor of 1792 and 217, using Euclidean algorithm.
Answer
The GCD of given numbers is 7.
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 still positive (), so we will continue with division.
Step 4 :
Divide by and get the remainder
The remainder is zero => GCD is the last divisor .
We can summarize an algorithm into a following table.
| 1792 | : | 217 | = | 8 | remainder ( 56 ) | ||||||
| 217 | : | 56 | = | 3 | remainder ( 49 ) | ||||||
| 56 | : | 49 | = | 1 | remainder ( 7 ) | ||||||
| 49 | : | 7 | = | 7 | remainder ( 0 ) | ||||||
| GCD = 7 | |||||||||||
This solution can be visualized using a Venn diagram.
0,0
1792
217
7
2
2
2
2
2
2
2
2
31
The GCD equals the product of the numbers at the intersection.
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