The GCD of given numbers is 1.
Step 1 :
Divide $ 14038 $ by $ 1529 $ and get the remainder
The remainder is positive ($ 277 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1529 $ by $ \color{blue}{ 277 } $ and get the remainder
The remainder is still positive ($ 144 > 0 $), so we will continue with division.
Step 3 :
Divide $ 277 $ by $ \color{blue}{ 144 } $ and get the remainder
The remainder is still positive ($ 133 > 0 $), so we will continue with division.
Step 4 :
Divide $ 144 $ by $ \color{blue}{ 133 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 5 :
Divide $ 133 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 11 $ 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.
14038 | : | 1529 | = | 9 | remainder ( 277 ) | ||||||||||
1529 | : | 277 | = | 5 | remainder ( 144 ) | ||||||||||
277 | : | 144 | = | 1 | remainder ( 133 ) | ||||||||||
144 | : | 133 | = | 1 | remainder ( 11 ) | ||||||||||
133 | : | 11 | = | 12 | remainder ( 1 ) | ||||||||||
11 | : | 1 | = | 11 | remainder ( 0 ) | ||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.