The GCD of given numbers is 2.
Step 1 :
Divide $ 4666 $ by $ 3454 $ and get the remainder
The remainder is positive ($ 1212 > 0 $), so we will continue with division.
Step 2 :
Divide $ 3454 $ by $ \color{blue}{ 1212 } $ and get the remainder
The remainder is still positive ($ 1030 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1212 $ by $ \color{blue}{ 1030 } $ and get the remainder
The remainder is still positive ($ 182 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1030 $ by $ \color{blue}{ 182 } $ and get the remainder
The remainder is still positive ($ 120 > 0 $), so we will continue with division.
Step 5 :
Divide $ 182 $ by $ \color{blue}{ 120 } $ and get the remainder
The remainder is still positive ($ 62 > 0 $), so we will continue with division.
Step 6 :
Divide $ 120 $ by $ \color{blue}{ 62 } $ and get the remainder
The remainder is still positive ($ 58 > 0 $), so we will continue with division.
Step 7 :
Divide $ 62 $ by $ \color{blue}{ 58 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 8 :
Divide $ 58 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 9 :
Divide $ 4 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
4666 | : | 3454 | = | 1 | remainder ( 1212 ) | ||||||||||||||||
3454 | : | 1212 | = | 2 | remainder ( 1030 ) | ||||||||||||||||
1212 | : | 1030 | = | 1 | remainder ( 182 ) | ||||||||||||||||
1030 | : | 182 | = | 5 | remainder ( 120 ) | ||||||||||||||||
182 | : | 120 | = | 1 | remainder ( 62 ) | ||||||||||||||||
120 | : | 62 | = | 1 | remainder ( 58 ) | ||||||||||||||||
62 | : | 58 | = | 1 | remainder ( 4 ) | ||||||||||||||||
58 | : | 4 | = | 14 | remainder ( 2 ) | ||||||||||||||||
4 | : | 2 | = | 2 | remainder ( 0 ) | ||||||||||||||||
GCD = 2 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.