Question
Find Greatest Common Divisor of 33 and 70, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
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.
| 70 | : | 33 | = | 2 | remainder ( 4 ) | ||||
| 33 | : | 4 | = | 8 | remainder ( 1 ) | ||||
| 4 | : | 1 | = | 4 | remainder ( 0 ) | ||||
| GCD = 1 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
33
70
1
3
11
2
5
7
The GCD equals the product of the numbers at the intersection.
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