The GCD of given numbers is 2.
Step 1 :
Divide $ 3210 $ by $ 1108 $ and get the remainder
The remainder is positive ($ 994 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1108 $ by $ \color{blue}{ 994 } $ and get the remainder
The remainder is still positive ($ 114 > 0 $), so we will continue with division.
Step 3 :
Divide $ 994 $ by $ \color{blue}{ 114 } $ and get the remainder
The remainder is still positive ($ 82 > 0 $), so we will continue with division.
Step 4 :
Divide $ 114 $ by $ \color{blue}{ 82 } $ and get the remainder
The remainder is still positive ($ 32 > 0 $), so we will continue with division.
Step 5 :
Divide $ 82 $ by $ \color{blue}{ 32 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 6 :
Divide $ 32 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 7 :
Divide $ 18 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 8 :
Divide $ 14 $ 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.
3210 | : | 1108 | = | 2 | remainder ( 994 ) | ||||||||||||||||
1108 | : | 994 | = | 1 | remainder ( 114 ) | ||||||||||||||||
994 | : | 114 | = | 8 | remainder ( 82 ) | ||||||||||||||||
114 | : | 82 | = | 1 | remainder ( 32 ) | ||||||||||||||||
82 | : | 32 | = | 2 | remainder ( 18 ) | ||||||||||||||||
32 | : | 18 | = | 1 | remainder ( 14 ) | ||||||||||||||||
18 | : | 14 | = | 1 | remainder ( 4 ) | ||||||||||||||||
14 | : | 4 | = | 3 | 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.