Question
Find Greatest Common Divisor of 53 and 28, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
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.
| 53 | : | 28 | = | 1 | remainder ( 25 ) | ||||||
| 28 | : | 25 | = | 1 | remainder ( 3 ) | ||||||
| 25 | : | 3 | = | 8 | remainder ( 1 ) | ||||||
| 3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
0,0
53
28
1
53
2
2
7
The GCD equals the product of the numbers at the intersection.
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