The GCD of given numbers is 24.
Step 1 :
Divide $ 696 $ by $ 432 $ and get the remainder
The remainder is positive ($ 264 > 0 $), so we will continue with division.
Step 2 :
Divide $ 432 $ by $ \color{blue}{ 264 } $ and get the remainder
The remainder is still positive ($ 168 > 0 $), so we will continue with division.
Step 3 :
Divide $ 264 $ by $ \color{blue}{ 168 } $ and get the remainder
The remainder is still positive ($ 96 > 0 $), so we will continue with division.
Step 4 :
Divide $ 168 $ by $ \color{blue}{ 96 } $ and get the remainder
The remainder is still positive ($ 72 > 0 $), so we will continue with division.
Step 5 :
Divide $ 96 $ by $ \color{blue}{ 72 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 6 :
Divide $ 72 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 24 }} $.
We can summarize an algorithm into a following table.
696 | : | 432 | = | 1 | remainder ( 264 ) | ||||||||||
432 | : | 264 | = | 1 | remainder ( 168 ) | ||||||||||
264 | : | 168 | = | 1 | remainder ( 96 ) | ||||||||||
168 | : | 96 | = | 1 | remainder ( 72 ) | ||||||||||
96 | : | 72 | = | 1 | remainder ( 24 ) | ||||||||||
72 | : | 24 | = | 3 | remainder ( 0 ) | ||||||||||
GCD = 24 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.