Question
Find Greatest Common Divisor of 13113 and 1410, using Euclidean algorithm.
Answer
The GCD of given numbers is 141.
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.
| 13113 | : | 1410 | = | 9 | remainder ( 423 ) | ||||
| 1410 | : | 423 | = | 3 | remainder ( 141 ) | ||||
| 423 | : | 141 | = | 3 | remainder ( 0 ) | ||||
| GCD = 141 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
13113
1410
3
47
3
31
2
5
The GCD equals the product of the numbers at the intersection.
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