The GCD of given numbers is 2.
Step 1 :
Divide $ 9512 $ by $ 3578 $ and get the remainder
The remainder is positive ($ 2356 > 0 $), so we will continue with division.
Step 2 :
Divide $ 3578 $ by $ \color{blue}{ 2356 } $ and get the remainder
The remainder is still positive ($ 1222 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2356 $ by $ \color{blue}{ 1222 } $ and get the remainder
The remainder is still positive ($ 1134 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1222 $ by $ \color{blue}{ 1134 } $ and get the remainder
The remainder is still positive ($ 88 > 0 $), so we will continue with division.
Step 5 :
Divide $ 1134 $ by $ \color{blue}{ 88 } $ and get the remainder
The remainder is still positive ($ 78 > 0 $), so we will continue with division.
Step 6 :
Divide $ 88 $ by $ \color{blue}{ 78 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 7 :
Divide $ 78 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 8 :
Divide $ 10 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 9 :
Divide $ 8 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
9512 | : | 3578 | = | 2 | remainder ( 2356 ) | ||||||||||||||||
3578 | : | 2356 | = | 1 | remainder ( 1222 ) | ||||||||||||||||
2356 | : | 1222 | = | 1 | remainder ( 1134 ) | ||||||||||||||||
1222 | : | 1134 | = | 1 | remainder ( 88 ) | ||||||||||||||||
1134 | : | 88 | = | 12 | remainder ( 78 ) | ||||||||||||||||
88 | : | 78 | = | 1 | remainder ( 10 ) | ||||||||||||||||
78 | : | 10 | = | 7 | remainder ( 8 ) | ||||||||||||||||
10 | : | 8 | = | 1 | remainder ( 2 ) | ||||||||||||||||
8 | : | 2 | = | 4 | remainder ( 0 ) | ||||||||||||||||
GCD = 2 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.