The GCD of given numbers is 12.
Step 1 :
Divide $ 1032 $ by $ 780 $ and get the remainder
The remainder is positive ($ 252 > 0 $), so we will continue with division.
Step 2 :
Divide $ 780 $ by $ \color{blue}{ 252 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 3 :
Divide $ 252 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 4 :
Divide $ 24 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 12 }} $.
We can summarize an algorithm into a following table.
1032 | : | 780 | = | 1 | remainder ( 252 ) | ||||||
780 | : | 252 | = | 3 | remainder ( 24 ) | ||||||
252 | : | 24 | = | 10 | remainder ( 12 ) | ||||||
24 | : | 12 | = | 2 | remainder ( 0 ) | ||||||
GCD = 12 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.