Question
Find Greatest Common Divisor of 1000 and 5040, using Euclidean algorithm.
Answer
The GCD of given numbers is 40.
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.
| 5040 | : | 1000 | = | 5 | remainder ( 40 ) | ||
| 1000 | : | 40 | = | 25 | remainder ( 0 ) | ||
| GCD = 40 | |||||||
This solution can be visualized using a Venn diagram.
0,0
1000
5040
2
2
2
5
5
5
2
3
3
7
The GCD equals the product of the numbers at the intersection.
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