Question
Find Greatest Common Divisor of 40 and 50, using Euclidean algorithm.
Answer
The GCD of given numbers is 10.
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.
| 50 | : | 40 | = | 1 | remainder ( 10 ) | ||
| 40 | : | 10 | = | 4 | remainder ( 0 ) | ||
| GCD = 10 | |||||||
This solution can be visualized using a Venn diagram.
0,0
40
50
2
5
2
2
5
The GCD equals the product of the numbers at the intersection.
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