Question
Find Greatest Common Divisor of 80 and 44, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
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 still positive (), so we will continue with division.
Step 4 :
Divide by and get the remainder
The remainder is zero => GCD is the last divisor .
We can summarize an algorithm into a following table.
| 80 | : | 44 | = | 1 | remainder ( 36 ) | ||||||
| 44 | : | 36 | = | 1 | remainder ( 8 ) | ||||||
| 36 | : | 8 | = | 4 | remainder ( 4 ) | ||||||
| 8 | : | 4 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 4 | |||||||||||
This solution can be visualized using a Venn diagram.
0,0
80
44
2
2
2
2
5
11
The GCD equals the product of the numbers at the intersection.
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