The GCD of given numbers is 1.
Step 1 :
Divide $ 1586 $ by $ 899 $ and get the remainder
The remainder is positive ($ 687 > 0 $), so we will continue with division.
Step 2 :
Divide $ 899 $ by $ \color{blue}{ 687 } $ and get the remainder
The remainder is still positive ($ 212 > 0 $), so we will continue with division.
Step 3 :
Divide $ 687 $ by $ \color{blue}{ 212 } $ and get the remainder
The remainder is still positive ($ 51 > 0 $), so we will continue with division.
Step 4 :
Divide $ 212 $ by $ \color{blue}{ 51 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 51 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 6 :
Divide $ 8 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 2 $ 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.
1586 | : | 899 | = | 1 | remainder ( 687 ) | ||||||||||||||
899 | : | 687 | = | 1 | remainder ( 212 ) | ||||||||||||||
687 | : | 212 | = | 3 | remainder ( 51 ) | ||||||||||||||
212 | : | 51 | = | 4 | remainder ( 8 ) | ||||||||||||||
51 | : | 8 | = | 6 | remainder ( 3 ) | ||||||||||||||
8 | : | 3 | = | 2 | remainder ( 2 ) | ||||||||||||||
3 | : | 2 | = | 1 | remainder ( 1 ) | ||||||||||||||
2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.