Question
Find Greatest Common Divisor of 133 and 38, using Euclidean algorithm.
Answer
The GCD of given numbers is 19.
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.
| 133 | : | 38 | = | 3 | remainder ( 19 ) | ||
| 38 | : | 19 | = | 2 | remainder ( 0 ) | ||
| GCD = 19 | |||||||
This solution can be visualized using a Venn diagram.
0,0
133
38
19
7
2
The GCD equals the product of the numbers at the intersection.
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