The GCD of given numbers is 37.
Step 1 :
Divide $ 1147 $ by $ 851 $ and get the remainder
The remainder is positive ($ 296 > 0 $), so we will continue with division.
Step 2 :
Divide $ 851 $ by $ \color{blue}{ 296 } $ and get the remainder
The remainder is still positive ($ 259 > 0 $), so we will continue with division.
Step 3 :
Divide $ 296 $ by $ \color{blue}{ 259 } $ and get the remainder
The remainder is still positive ($ 37 > 0 $), so we will continue with division.
Step 4 :
Divide $ 259 $ by $ \color{blue}{ 37 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 37 }} $.
We can summarize an algorithm into a following table.
1147 | : | 851 | = | 1 | remainder ( 296 ) | ||||||
851 | : | 296 | = | 2 | remainder ( 259 ) | ||||||
296 | : | 259 | = | 1 | remainder ( 37 ) | ||||||
259 | : | 37 | = | 7 | remainder ( 0 ) | ||||||
GCD = 37 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.