Question
Find Greatest Common Divisor of 117 and 65, using Euclidean algorithm.
Answer
The GCD of given numbers is 13.
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.
| 117 | : | 65 | = | 1 | remainder ( 52 ) | ||||
| 65 | : | 52 | = | 1 | remainder ( 13 ) | ||||
| 52 | : | 13 | = | 4 | remainder ( 0 ) | ||||
| GCD = 13 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
117
65
13
3
3
5
The GCD equals the product of the numbers at the intersection.
This page was created using
GCD Calculator