The GCD of given numbers is 1.
Step 1 :
Divide $ 3299 $ by $ 647 $ and get the remainder
The remainder is positive ($ 64 > 0 $), so we will continue with division.
Step 2 :
Divide $ 647 $ by $ \color{blue}{ 64 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 3 :
Divide $ 64 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 7 $ 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.
3299 | : | 647 | = | 5 | remainder ( 64 ) | ||||||
647 | : | 64 | = | 10 | remainder ( 7 ) | ||||||
64 | : | 7 | = | 9 | remainder ( 1 ) | ||||||
7 | : | 1 | = | 7 | remainder ( 0 ) | ||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.