The GCD of given numbers is 1.
Step 1 :
Divide $ 415 $ by $ 142 $ and get the remainder
The remainder is positive ($ 131 > 0 $), so we will continue with division.
Step 2 :
Divide $ 142 $ by $ \color{blue}{ 131 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 3 :
Divide $ 131 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 4 :
Divide $ 11 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 10 $ 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.
415 | : | 142 | = | 2 | remainder ( 131 ) | ||||||||
142 | : | 131 | = | 1 | remainder ( 11 ) | ||||||||
131 | : | 11 | = | 11 | remainder ( 10 ) | ||||||||
11 | : | 10 | = | 1 | remainder ( 1 ) | ||||||||
10 | : | 1 | = | 10 | remainder ( 0 ) | ||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.