Question
Find Greatest Common Divisor of 72 and 15, 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.
| 72 | : | 15 | = | 4 | remainder ( 12 ) | ||||
| 15 | : | 12 | = | 1 | remainder ( 3 ) | ||||
| 12 | : | 3 | = | 4 | remainder ( 0 ) | ||||
| GCD = 3 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
72
15
3
2
2
2
3
5
The GCD equals the product of the numbers at the intersection.
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