Find Greatest Common Divisor of 105 and 33, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 105 $ by $ 33 $ and get the remainder
The remainder is positive ($ 6 > 0 $), so we will continue with division.
Step 2 :
Divide $ 33 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 3 :
Divide $ 6 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
| 105 | : | 33 | = | 3 | remainder ( 6 ) | ||||
| 33 | : | 6 | = | 5 | remainder ( 3 ) | ||||
| 6 | : | 3 | = | 2 | remainder ( 0 ) | ||||
| GCD = 3 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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