The GCD of given numbers is 1.
Step 1 :
Divide $ 2468 $ by $ 1357 $ and get the remainder
The remainder is positive ($ 1111 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1357 $ by $ \color{blue}{ 1111 } $ and get the remainder
The remainder is still positive ($ 246 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1111 $ by $ \color{blue}{ 246 } $ and get the remainder
The remainder is still positive ($ 127 > 0 $), so we will continue with division.
Step 4 :
Divide $ 246 $ by $ \color{blue}{ 127 } $ and get the remainder
The remainder is still positive ($ 119 > 0 $), so we will continue with division.
Step 5 :
Divide $ 127 $ by $ \color{blue}{ 119 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 6 :
Divide $ 119 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 7 :
Divide $ 8 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 7 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
2468 | : | 1357 | = | 1 | remainder ( 1111 ) | ||||||||||||||
1357 | : | 1111 | = | 1 | remainder ( 246 ) | ||||||||||||||
1111 | : | 246 | = | 4 | remainder ( 127 ) | ||||||||||||||
246 | : | 127 | = | 1 | remainder ( 119 ) | ||||||||||||||
127 | : | 119 | = | 1 | remainder ( 8 ) | ||||||||||||||
119 | : | 8 | = | 14 | remainder ( 7 ) | ||||||||||||||
8 | : | 7 | = | 1 | remainder ( 1 ) | ||||||||||||||
7 | : | 1 | = | 7 | remainder ( 0 ) | ||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.