The GCD of given numbers is 1.
Step 1 :
Divide $ 42905 $ by $ 12906 $ and get the remainder
The remainder is positive ($ 4187 > 0 $), so we will continue with division.
Step 2 :
Divide $ 12906 $ by $ \color{blue}{ 4187 } $ and get the remainder
The remainder is still positive ($ 345 > 0 $), so we will continue with division.
Step 3 :
Divide $ 4187 $ by $ \color{blue}{ 345 } $ and get the remainder
The remainder is still positive ($ 47 > 0 $), so we will continue with division.
Step 4 :
Divide $ 345 $ by $ \color{blue}{ 47 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 5 :
Divide $ 47 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 6 :
Divide $ 16 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
Divide $ 15 $ 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.
42905 | : | 12906 | = | 3 | remainder ( 4187 ) | ||||||||||||
12906 | : | 4187 | = | 3 | remainder ( 345 ) | ||||||||||||
4187 | : | 345 | = | 12 | remainder ( 47 ) | ||||||||||||
345 | : | 47 | = | 7 | remainder ( 16 ) | ||||||||||||
47 | : | 16 | = | 2 | remainder ( 15 ) | ||||||||||||
16 | : | 15 | = | 1 | remainder ( 1 ) | ||||||||||||
15 | : | 1 | = | 15 | remainder ( 0 ) | ||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.