The GCD of given numbers is 27.
Step 1 :
Divide $ 41445 $ by $ 4806 $ and get the remainder
The remainder is positive ($ 2997 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4806 $ by $ \color{blue}{ 2997 } $ and get the remainder
The remainder is still positive ($ 1809 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2997 $ by $ \color{blue}{ 1809 } $ and get the remainder
The remainder is still positive ($ 1188 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1809 $ by $ \color{blue}{ 1188 } $ and get the remainder
The remainder is still positive ($ 621 > 0 $), so we will continue with division.
Step 5 :
Divide $ 1188 $ by $ \color{blue}{ 621 } $ and get the remainder
The remainder is still positive ($ 567 > 0 $), so we will continue with division.
Step 6 :
Divide $ 621 $ by $ \color{blue}{ 567 } $ and get the remainder
The remainder is still positive ($ 54 > 0 $), so we will continue with division.
Step 7 :
Divide $ 567 $ by $ \color{blue}{ 54 } $ and get the remainder
The remainder is still positive ($ 27 > 0 $), so we will continue with division.
Step 8 :
Divide $ 54 $ by $ \color{blue}{ 27 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 27 }} $.
We can summarize an algorithm into a following table.
41445 | : | 4806 | = | 8 | remainder ( 2997 ) | ||||||||||||||
4806 | : | 2997 | = | 1 | remainder ( 1809 ) | ||||||||||||||
2997 | : | 1809 | = | 1 | remainder ( 1188 ) | ||||||||||||||
1809 | : | 1188 | = | 1 | remainder ( 621 ) | ||||||||||||||
1188 | : | 621 | = | 1 | remainder ( 567 ) | ||||||||||||||
621 | : | 567 | = | 1 | remainder ( 54 ) | ||||||||||||||
567 | : | 54 | = | 10 | remainder ( 27 ) | ||||||||||||||
54 | : | 27 | = | 2 | remainder ( 0 ) | ||||||||||||||
GCD = 27 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.