The GCD of given numbers is 1.
Step 1 :
Divide $ 179 $ by $ 142 $ and get the remainder
The remainder is positive ($ 37 > 0 $), so we will continue with division.
Step 2 :
Divide $ 142 $ by $ \color{blue}{ 37 } $ and get the remainder
The remainder is still positive ($ 31 > 0 $), so we will continue with division.
Step 3 :
Divide $ 37 $ by $ \color{blue}{ 31 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 31 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 6 $ 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.
179 | : | 142 | = | 1 | remainder ( 37 ) | ||||||||
142 | : | 37 | = | 3 | remainder ( 31 ) | ||||||||
37 | : | 31 | = | 1 | remainder ( 6 ) | ||||||||
31 | : | 6 | = | 5 | remainder ( 1 ) | ||||||||
6 | : | 1 | = | 6 | remainder ( 0 ) | ||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.