The GCD of given numbers is 2.
Step 1 :
Divide $ 976 $ by $ 174 $ and get the remainder
The remainder is positive ($ 106 > 0 $), so we will continue with division.
Step 2 :
Divide $ 174 $ by $ \color{blue}{ 106 } $ and get the remainder
The remainder is still positive ($ 68 > 0 $), so we will continue with division.
Step 3 :
Divide $ 106 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 38 > 0 $), so we will continue with division.
Step 4 :
Divide $ 68 $ by $ \color{blue}{ 38 } $ and get the remainder
The remainder is still positive ($ 30 > 0 $), so we will continue with division.
Step 5 :
Divide $ 38 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 6 :
Divide $ 30 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 7 :
Divide $ 8 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 8 :
Divide $ 6 $ 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.
976 | : | 174 | = | 5 | remainder ( 106 ) | ||||||||||||||
174 | : | 106 | = | 1 | remainder ( 68 ) | ||||||||||||||
106 | : | 68 | = | 1 | remainder ( 38 ) | ||||||||||||||
68 | : | 38 | = | 1 | remainder ( 30 ) | ||||||||||||||
38 | : | 30 | = | 1 | remainder ( 8 ) | ||||||||||||||
30 | : | 8 | = | 3 | remainder ( 6 ) | ||||||||||||||
8 | : | 6 | = | 1 | remainder ( 2 ) | ||||||||||||||
6 | : | 2 | = | 3 | remainder ( 0 ) | ||||||||||||||
GCD = 2 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.