The GCD of given numbers is 8.
Step 1 :
Divide $ 19520 $ by $ 2312 $ and get the remainder
The remainder is positive ($ 1024 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2312 $ by $ \color{blue}{ 1024 } $ and get the remainder
The remainder is still positive ($ 264 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1024 $ by $ \color{blue}{ 264 } $ and get the remainder
The remainder is still positive ($ 232 > 0 $), so we will continue with division.
Step 4 :
Divide $ 264 $ by $ \color{blue}{ 232 } $ and get the remainder
The remainder is still positive ($ 32 > 0 $), so we will continue with division.
Step 5 :
Divide $ 232 $ by $ \color{blue}{ 32 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 6 :
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.
19520 | : | 2312 | = | 8 | remainder ( 1024 ) | ||||||||||
2312 | : | 1024 | = | 2 | remainder ( 264 ) | ||||||||||
1024 | : | 264 | = | 3 | remainder ( 232 ) | ||||||||||
264 | : | 232 | = | 1 | remainder ( 32 ) | ||||||||||
232 | : | 32 | = | 7 | 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.