Question
Find Greatest Common Divisor of 972 and 783, using Euclidean algorithm.
Answer
The GCD of given numbers is 27.
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.
| 972 | : | 783 | = | 1 | remainder ( 189 ) | ||||
| 783 | : | 189 | = | 4 | remainder ( 27 ) | ||||
| 189 | : | 27 | = | 7 | remainder ( 0 ) | ||||
| GCD = 27 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
972
783
3
3
3
2
2
3
3
29
The GCD equals the product of the numbers at the intersection.
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