Question
Find Greatest Common Divisor of 28 and 52, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
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.
| 52 | : | 28 | = | 1 | remainder ( 24 ) | ||||
| 28 | : | 24 | = | 1 | remainder ( 4 ) | ||||
| 24 | : | 4 | = | 6 | remainder ( 0 ) | ||||
| GCD = 4 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
28
52
2
2
7
13
The GCD equals the product of the numbers at the intersection.
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