Question
Find Greatest Common Divisor of 63 and 90, using Euclidean algorithm.
Answer
The GCD of given numbers is 9.
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.
| 90 | : | 63 | = | 1 | remainder ( 27 ) | ||||
| 63 | : | 27 | = | 2 | remainder ( 9 ) | ||||
| 27 | : | 9 | = | 3 | remainder ( 0 ) | ||||
| GCD = 9 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
63
90
3
3
7
2
5
The GCD equals the product of the numbers at the intersection.
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