The GCD of given numbers is 1078.
Step 1 :
Divide $ 1160718174 $ by $ 316258250 $ and get the remainder
The remainder is positive ($ 211943424 > 0 $), so we will continue with division.
Step 2 :
Divide $ 316258250 $ by $ \color{blue}{ 211943424 } $ and get the remainder
The remainder is still positive ($ 104314826 > 0 $), so we will continue with division.
Step 3 :
Divide $ 211943424 $ by $ \color{blue}{ 104314826 } $ and get the remainder
The remainder is still positive ($ 3313772 > 0 $), so we will continue with division.
Step 4 :
Divide $ 104314826 $ by $ \color{blue}{ 3313772 } $ and get the remainder
The remainder is still positive ($ 1587894 > 0 $), so we will continue with division.
Step 5 :
Divide $ 3313772 $ by $ \color{blue}{ 1587894 } $ and get the remainder
The remainder is still positive ($ 137984 > 0 $), so we will continue with division.
Step 6 :
Divide $ 1587894 $ by $ \color{blue}{ 137984 } $ and get the remainder
The remainder is still positive ($ 70070 > 0 $), so we will continue with division.
Step 7 :
Divide $ 137984 $ by $ \color{blue}{ 70070 } $ and get the remainder
The remainder is still positive ($ 67914 > 0 $), so we will continue with division.
Step 8 :
Divide $ 70070 $ by $ \color{blue}{ 67914 } $ and get the remainder
The remainder is still positive ($ 2156 > 0 $), so we will continue with division.
Step 9 :
Divide $ 67914 $ by $ \color{blue}{ 2156 } $ and get the remainder
The remainder is still positive ($ 1078 > 0 $), so we will continue with division.
Step 10 :
Divide $ 2156 $ by $ \color{blue}{ 1078 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1078 }} $.
We can summarize an algorithm into a following table.
1160718174 | : | 316258250 | = | 3 | remainder ( 211943424 ) | ||||||||||||||||||
316258250 | : | 211943424 | = | 1 | remainder ( 104314826 ) | ||||||||||||||||||
211943424 | : | 104314826 | = | 2 | remainder ( 3313772 ) | ||||||||||||||||||
104314826 | : | 3313772 | = | 31 | remainder ( 1587894 ) | ||||||||||||||||||
3313772 | : | 1587894 | = | 2 | remainder ( 137984 ) | ||||||||||||||||||
1587894 | : | 137984 | = | 11 | remainder ( 70070 ) | ||||||||||||||||||
137984 | : | 70070 | = | 1 | remainder ( 67914 ) | ||||||||||||||||||
70070 | : | 67914 | = | 1 | remainder ( 2156 ) | ||||||||||||||||||
67914 | : | 2156 | = | 31 | remainder ( 1078 ) | ||||||||||||||||||
2156 | : | 1078 | = | 2 | remainder ( 0 ) | ||||||||||||||||||
GCD = 1078 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.