The GCD of given numbers is 8.
Step 1 :
Divide $ 4424 $ by $ 864 $ and get the remainder
The remainder is positive ($ 104 > 0 $), so we will continue with division.
Step 2 :
Divide $ 864 $ by $ \color{blue}{ 104 } $ and get the remainder
The remainder is still positive ($ 32 > 0 $), so we will continue with division.
Step 3 :
Divide $ 104 $ by $ \color{blue}{ 32 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 4 :
Divide $ 32 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.
We can summarize an algorithm into a following table.
4424 | : | 864 | = | 5 | remainder ( 104 ) | ||||||
864 | : | 104 | = | 8 | remainder ( 32 ) | ||||||
104 | : | 32 | = | 3 | remainder ( 8 ) | ||||||
32 | : | 8 | = | 4 | remainder ( 0 ) | ||||||
GCD = 8 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.