The GCD of given numbers is 1.
Step 1 :
Divide $ 2435 $ by $ 342 $ and get the remainder
The remainder is positive ($ 41 > 0 $), so we will continue with division.
Step 2 :
Divide $ 342 $ by $ \color{blue}{ 41 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 3 :
Divide $ 41 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 4 :
Divide $ 14 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 13 $ 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.
2435 | : | 342 | = | 7 | remainder ( 41 ) | ||||||||
342 | : | 41 | = | 8 | remainder ( 14 ) | ||||||||
41 | : | 14 | = | 2 | remainder ( 13 ) | ||||||||
14 | : | 13 | = | 1 | remainder ( 1 ) | ||||||||
13 | : | 1 | = | 13 | remainder ( 0 ) | ||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.