Question
Find Greatest Common Divisor of 1001 and 1331, using Euclidean algorithm.
Answer
The GCD of given numbers is 11.
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.
| 1331 | : | 1001 | = | 1 | remainder ( 330 ) | ||||
| 1001 | : | 330 | = | 3 | remainder ( 11 ) | ||||
| 330 | : | 11 | = | 30 | remainder ( 0 ) | ||||
| GCD = 11 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
1001
1331
11
7
13
11
11
The GCD equals the product of the numbers at the intersection.
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