Question
Find Greatest Common Divisor of 1461 and 117, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
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.
| 1461 | : | 117 | = | 12 | remainder ( 57 ) | ||||
| 117 | : | 57 | = | 2 | remainder ( 3 ) | ||||
| 57 | : | 3 | = | 19 | remainder ( 0 ) | ||||
| GCD = 3 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
1461
117
3
487
3
13
The GCD equals the product of the numbers at the intersection.
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