Find Greatest Common Divisor of 29106 and 5382, using Euclidean algorithm.
Answer
The GCD of given numbers is 18.
Explanation
Step 1 :
Divide $ 29106 $ by $ 5382 $ and get the remainder
The remainder is positive ($ 2196 > 0 $), so we will continue with division.
Step 2 :
Divide $ 5382 $ by $ \color{blue}{ 2196 } $ and get the remainder
The remainder is still positive ($ 990 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2196 $ by $ \color{blue}{ 990 } $ and get the remainder
The remainder is still positive ($ 216 > 0 $), so we will continue with division.
Step 4 :
Divide $ 990 $ by $ \color{blue}{ 216 } $ and get the remainder
The remainder is still positive ($ 126 > 0 $), so we will continue with division.
Step 5 :
Divide $ 216 $ by $ \color{blue}{ 126 } $ and get the remainder
The remainder is still positive ($ 90 > 0 $), so we will continue with division.
Step 6 :
Divide $ 126 $ by $ \color{blue}{ 90 } $ and get the remainder
The remainder is still positive ($ 36 > 0 $), so we will continue with division.
Step 7 :
Divide $ 90 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 8 :
Divide $ 36 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 18 }} $.
We can summarize an algorithm into a following table.
| 29106 | : | 5382 | = | 5 | remainder ( 2196 ) | ||||||||||||||
| 5382 | : | 2196 | = | 2 | remainder ( 990 ) | ||||||||||||||
| 2196 | : | 990 | = | 2 | remainder ( 216 ) | ||||||||||||||
| 990 | : | 216 | = | 4 | remainder ( 126 ) | ||||||||||||||
| 216 | : | 126 | = | 1 | remainder ( 90 ) | ||||||||||||||
| 126 | : | 90 | = | 1 | remainder ( 36 ) | ||||||||||||||
| 90 | : | 36 | = | 2 | remainder ( 18 ) | ||||||||||||||
| 36 | : | 18 | = | 2 | remainder ( 0 ) | ||||||||||||||
| GCD = 18 | |||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.