The GCD of given numbers is 1.
Step 1 :
Divide $ 4231 $ by $ 1100 $ and get the remainder
The remainder is positive ($ 931 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1100 $ by $ \color{blue}{ 931 } $ and get the remainder
The remainder is still positive ($ 169 > 0 $), so we will continue with division.
Step 3 :
Divide $ 931 $ by $ \color{blue}{ 169 } $ and get the remainder
The remainder is still positive ($ 86 > 0 $), so we will continue with division.
Step 4 :
Divide $ 169 $ by $ \color{blue}{ 86 } $ and get the remainder
The remainder is still positive ($ 83 > 0 $), so we will continue with division.
Step 5 :
Divide $ 86 $ by $ \color{blue}{ 83 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 6 :
Divide $ 83 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
4231 | : | 1100 | = | 3 | remainder ( 931 ) | ||||||||||||||
1100 | : | 931 | = | 1 | remainder ( 169 ) | ||||||||||||||
931 | : | 169 | = | 5 | remainder ( 86 ) | ||||||||||||||
169 | : | 86 | = | 1 | remainder ( 83 ) | ||||||||||||||
86 | : | 83 | = | 1 | remainder ( 3 ) | ||||||||||||||
83 | : | 3 | = | 27 | remainder ( 2 ) | ||||||||||||||
3 | : | 2 | = | 1 | remainder ( 1 ) | ||||||||||||||
2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.