Question
Find Greatest Common Divisor of 1875 and 135, using Euclidean algorithm.
Answer
The GCD of given numbers is 15.
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.
| 1875 | : | 135 | = | 13 | remainder ( 120 ) | ||||
| 135 | : | 120 | = | 1 | remainder ( 15 ) | ||||
| 120 | : | 15 | = | 8 | remainder ( 0 ) | ||||
| GCD = 15 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
1875
135
3
5
5
5
5
3
3
The GCD equals the product of the numbers at the intersection.
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