Question
Find Greatest Common Divisor of 52 and 39, using Euclidean algorithm.
Answer
The GCD of given numbers is 13.
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 zero => GCD is the last divisor .
We can summarize an algorithm into a following table.
| 52 | : | 39 | = | 1 | remainder ( 13 ) | ||
| 39 | : | 13 | = | 3 | remainder ( 0 ) | ||
| GCD = 13 | |||||||
This solution can be visualized using a Venn diagram.
0,0
52
39
13
2
2
3
The GCD equals the product of the numbers at the intersection.
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