Question
Find Greatest Common Divisor of 506 and 2185, using Euclidean algorithm.
Answer
The GCD of given numbers is 23.
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.
| 2185 | : | 506 | = | 4 | remainder ( 161 ) | ||||
| 506 | : | 161 | = | 3 | remainder ( 23 ) | ||||
| 161 | : | 23 | = | 7 | remainder ( 0 ) | ||||
| GCD = 23 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
506
2185
23
2
11
5
19
The GCD equals the product of the numbers at the intersection.
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