Question
Find Greatest Common Divisor of 21 and 2511, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
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.
| 2511 | : | 21 | = | 119 | remainder ( 12 ) | ||||||
| 21 | : | 12 | = | 1 | remainder ( 9 ) | ||||||
| 12 | : | 9 | = | 1 | remainder ( 3 ) | ||||||
| 9 | : | 3 | = | 3 | remainder ( 0 ) | ||||||
| GCD = 3 | |||||||||||
This solution can be visualized using a Venn diagram.
0,0
21
2511
3
7
3
3
3
31
The GCD equals the product of the numbers at the intersection.
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