Question
Find Greatest Common Divisor of 10001 and 100083, using Euclidean algorithm.
Answer
The GCD of given numbers is 73.
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.
| 100083 | : | 10001 | = | 10 | remainder ( 73 ) | ||
| 10001 | : | 73 | = | 137 | remainder ( 0 ) | ||
| GCD = 73 | |||||||
This solution can be visualized using a Venn diagram.
0,0
10001
100083
73
137
3
457
The GCD equals the product of the numbers at the intersection.
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