The GCD of given numbers is 17.
Step 1 :
Divide $ 1105 $ by $ 238 $ and get the remainder
The remainder is positive ($ 153 > 0 $), so we will continue with division.
Step 2 :
Divide $ 238 $ by $ \color{blue}{ 153 } $ and get the remainder
The remainder is still positive ($ 85 > 0 $), so we will continue with division.
Step 3 :
Divide $ 153 $ by $ \color{blue}{ 85 } $ and get the remainder
The remainder is still positive ($ 68 > 0 $), so we will continue with division.
Step 4 :
Divide $ 85 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 5 :
Divide $ 68 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 17 }} $.
We can summarize an algorithm into a following table.
1105 | : | 238 | = | 4 | remainder ( 153 ) | ||||||||
238 | : | 153 | = | 1 | remainder ( 85 ) | ||||||||
153 | : | 85 | = | 1 | remainder ( 68 ) | ||||||||
85 | : | 68 | = | 1 | remainder ( 17 ) | ||||||||
68 | : | 17 | = | 4 | remainder ( 0 ) | ||||||||
GCD = 17 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.