Find Greatest Common Divisor of 11607 and 3162, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 11607 $ by $ 3162 $ and get the remainder
The remainder is positive ($ 2121 > 0 $), so we will continue with division.
Step 2 :
Divide $ 3162 $ by $ \color{blue}{ 2121 } $ and get the remainder
The remainder is still positive ($ 1041 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2121 $ by $ \color{blue}{ 1041 } $ and get the remainder
The remainder is still positive ($ 39 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1041 $ by $ \color{blue}{ 39 } $ and get the remainder
The remainder is still positive ($ 27 > 0 $), so we will continue with division.
Step 5 :
Divide $ 39 $ by $ \color{blue}{ 27 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 6 :
Divide $ 27 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 7 :
Divide $ 12 $ 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.
| 11607 | : | 3162 | = | 3 | remainder ( 2121 ) | ||||||||||||
| 3162 | : | 2121 | = | 1 | remainder ( 1041 ) | ||||||||||||
| 2121 | : | 1041 | = | 2 | remainder ( 39 ) | ||||||||||||
| 1041 | : | 39 | = | 26 | remainder ( 27 ) | ||||||||||||
| 39 | : | 27 | = | 1 | remainder ( 12 ) | ||||||||||||
| 27 | : | 12 | = | 2 | remainder ( 3 ) | ||||||||||||
| 12 | : | 3 | = | 4 | remainder ( 0 ) | ||||||||||||
| GCD = 3 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.