The GCD of given numbers is 1.
Step 1 :
Divide $ 857 $ by $ 239 $ and get the remainder
The remainder is positive ($ 140 > 0 $), so we will continue with division.
Step 2 :
Divide $ 239 $ by $ \color{blue}{ 140 } $ and get the remainder
The remainder is still positive ($ 99 > 0 $), so we will continue with division.
Step 3 :
Divide $ 140 $ by $ \color{blue}{ 99 } $ and get the remainder
The remainder is still positive ($ 41 > 0 $), so we will continue with division.
Step 4 :
Divide $ 99 $ by $ \color{blue}{ 41 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 5 :
Divide $ 41 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 6 :
Divide $ 17 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 7 :
Divide $ 7 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 3 $ 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.
857 | : | 239 | = | 3 | remainder ( 140 ) | ||||||||||||||
239 | : | 140 | = | 1 | remainder ( 99 ) | ||||||||||||||
140 | : | 99 | = | 1 | remainder ( 41 ) | ||||||||||||||
99 | : | 41 | = | 2 | remainder ( 17 ) | ||||||||||||||
41 | : | 17 | = | 2 | remainder ( 7 ) | ||||||||||||||
17 | : | 7 | = | 2 | remainder ( 3 ) | ||||||||||||||
7 | : | 3 | = | 2 | remainder ( 1 ) | ||||||||||||||
3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.