Question
Find Greatest Common Divisor of 557 and 239, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
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.
| 557 | : | 239 | = | 2 | remainder ( 79 ) | ||||||
| 239 | : | 79 | = | 3 | remainder ( 2 ) | ||||||
| 79 | : | 2 | = | 39 | remainder ( 1 ) | ||||||
| 2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
0,0
557
239
1
557
239
The GCD equals the product of the numbers at the intersection.
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