The GCD of given numbers is 7.
Step 1 :
Divide $ 987 $ by $ 343 $ and get the remainder
The remainder is positive ($ 301 > 0 $), so we will continue with division.
Step 2 :
Divide $ 343 $ by $ \color{blue}{ 301 } $ and get the remainder
The remainder is still positive ($ 42 > 0 $), so we will continue with division.
Step 3 :
Divide $ 301 $ by $ \color{blue}{ 42 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 4 :
Divide $ 42 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
987 | : | 343 | = | 2 | remainder ( 301 ) | ||||||
343 | : | 301 | = | 1 | remainder ( 42 ) | ||||||
301 | : | 42 | = | 7 | remainder ( 7 ) | ||||||
42 | : | 7 | = | 6 | remainder ( 0 ) | ||||||
GCD = 7 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.