The GCD of given numbers is 1.
Step 1 :
Divide $ 11846 $ by $ 6825 $ and get the remainder
The remainder is positive ($ 5021 > 0 $), so we will continue with division.
Step 2 :
Divide $ 6825 $ by $ \color{blue}{ 5021 } $ and get the remainder
The remainder is still positive ($ 1804 > 0 $), so we will continue with division.
Step 3 :
Divide $ 5021 $ by $ \color{blue}{ 1804 } $ and get the remainder
The remainder is still positive ($ 1413 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1804 $ by $ \color{blue}{ 1413 } $ and get the remainder
The remainder is still positive ($ 391 > 0 $), so we will continue with division.
Step 5 :
Divide $ 1413 $ by $ \color{blue}{ 391 } $ and get the remainder
The remainder is still positive ($ 240 > 0 $), so we will continue with division.
Step 6 :
Divide $ 391 $ by $ \color{blue}{ 240 } $ and get the remainder
The remainder is still positive ($ 151 > 0 $), so we will continue with division.
Step 7 :
Divide $ 240 $ by $ \color{blue}{ 151 } $ and get the remainder
The remainder is still positive ($ 89 > 0 $), so we will continue with division.
Step 8 :
Divide $ 151 $ by $ \color{blue}{ 89 } $ and get the remainder
The remainder is still positive ($ 62 > 0 $), so we will continue with division.
Step 9 :
Divide $ 89 $ by $ \color{blue}{ 62 } $ and get the remainder
The remainder is still positive ($ 27 > 0 $), so we will continue with division.
Step 10 :
Divide $ 62 $ by $ \color{blue}{ 27 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 11 :
Divide $ 27 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 12 :
Divide $ 8 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 13 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 14 :
Divide $ 2 $ 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.
11846 | : | 6825 | = | 1 | remainder ( 5021 ) | ||||||||||||||||||||||||||
6825 | : | 5021 | = | 1 | remainder ( 1804 ) | ||||||||||||||||||||||||||
5021 | : | 1804 | = | 2 | remainder ( 1413 ) | ||||||||||||||||||||||||||
1804 | : | 1413 | = | 1 | remainder ( 391 ) | ||||||||||||||||||||||||||
1413 | : | 391 | = | 3 | remainder ( 240 ) | ||||||||||||||||||||||||||
391 | : | 240 | = | 1 | remainder ( 151 ) | ||||||||||||||||||||||||||
240 | : | 151 | = | 1 | remainder ( 89 ) | ||||||||||||||||||||||||||
151 | : | 89 | = | 1 | remainder ( 62 ) | ||||||||||||||||||||||||||
89 | : | 62 | = | 1 | remainder ( 27 ) | ||||||||||||||||||||||||||
62 | : | 27 | = | 2 | remainder ( 8 ) | ||||||||||||||||||||||||||
27 | : | 8 | = | 3 | remainder ( 3 ) | ||||||||||||||||||||||||||
8 | : | 3 | = | 2 | remainder ( 2 ) | ||||||||||||||||||||||||||
3 | : | 2 | = | 1 | remainder ( 1 ) | ||||||||||||||||||||||||||
2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||||||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.