The GCD of given numbers is 2.
Step 1 :
Divide $ 1120 $ by $ 442 $ and get the remainder
The remainder is positive ($ 236 > 0 $), so we will continue with division.
Step 2 :
Divide $ 442 $ by $ \color{blue}{ 236 } $ and get the remainder
The remainder is still positive ($ 206 > 0 $), so we will continue with division.
Step 3 :
Divide $ 236 $ by $ \color{blue}{ 206 } $ and get the remainder
The remainder is still positive ($ 30 > 0 $), so we will continue with division.
Step 4 :
Divide $ 206 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 26 > 0 $), so we will continue with division.
Step 5 :
Divide $ 30 $ by $ \color{blue}{ 26 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 26 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
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.
1120 | : | 442 | = | 2 | remainder ( 236 ) | ||||||||||||
442 | : | 236 | = | 1 | remainder ( 206 ) | ||||||||||||
236 | : | 206 | = | 1 | remainder ( 30 ) | ||||||||||||
206 | : | 30 | = | 6 | remainder ( 26 ) | ||||||||||||
30 | : | 26 | = | 1 | remainder ( 4 ) | ||||||||||||
26 | : | 4 | = | 6 | 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.