Question
Find Greatest Common Divisor of 91 and 287, using Euclidean algorithm.
Answer
The GCD of given numbers is 7.
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.
| 287 | : | 91 | = | 3 | remainder ( 14 ) | ||||
| 91 | : | 14 | = | 6 | remainder ( 7 ) | ||||
| 14 | : | 7 | = | 2 | remainder ( 0 ) | ||||
| GCD = 7 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
91
287
7
13
41
The GCD equals the product of the numbers at the intersection.
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