The GCD of given numbers is 68.
Step 1 :
Divide $ 7684 $ by $ 4148 $ and get the remainder
The remainder is positive ($ 3536 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4148 $ by $ \color{blue}{ 3536 } $ and get the remainder
The remainder is still positive ($ 612 > 0 $), so we will continue with division.
Step 3 :
Divide $ 3536 $ by $ \color{blue}{ 612 } $ and get the remainder
The remainder is still positive ($ 476 > 0 $), so we will continue with division.
Step 4 :
Divide $ 612 $ by $ \color{blue}{ 476 } $ and get the remainder
The remainder is still positive ($ 136 > 0 $), so we will continue with division.
Step 5 :
Divide $ 476 $ by $ \color{blue}{ 136 } $ and get the remainder
The remainder is still positive ($ 68 > 0 $), so we will continue with division.
Step 6 :
Divide $ 136 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 68 }} $.
We can summarize an algorithm into a following table.
7684 | : | 4148 | = | 1 | remainder ( 3536 ) | ||||||||||
4148 | : | 3536 | = | 1 | remainder ( 612 ) | ||||||||||
3536 | : | 612 | = | 5 | remainder ( 476 ) | ||||||||||
612 | : | 476 | = | 1 | remainder ( 136 ) | ||||||||||
476 | : | 136 | = | 3 | remainder ( 68 ) | ||||||||||
136 | : | 68 | = | 2 | remainder ( 0 ) | ||||||||||
GCD = 68 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.