The GCD of given numbers is 3.
Step 1 :
Divide $ 2544 $ by $ 2001 $ and get the remainder
The remainder is positive ($ 543 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2001 $ by $ \color{blue}{ 543 } $ and get the remainder
The remainder is still positive ($ 372 > 0 $), so we will continue with division.
Step 3 :
Divide $ 543 $ by $ \color{blue}{ 372 } $ and get the remainder
The remainder is still positive ($ 171 > 0 $), so we will continue with division.
Step 4 :
Divide $ 372 $ by $ \color{blue}{ 171 } $ and get the remainder
The remainder is still positive ($ 30 > 0 $), so we will continue with division.
Step 5 :
Divide $ 171 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 6 :
Divide $ 30 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 7 :
Divide $ 21 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 8 :
Divide $ 9 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
2544 | : | 2001 | = | 1 | remainder ( 543 ) | ||||||||||||||
2001 | : | 543 | = | 3 | remainder ( 372 ) | ||||||||||||||
543 | : | 372 | = | 1 | remainder ( 171 ) | ||||||||||||||
372 | : | 171 | = | 2 | remainder ( 30 ) | ||||||||||||||
171 | : | 30 | = | 5 | remainder ( 21 ) | ||||||||||||||
30 | : | 21 | = | 1 | remainder ( 9 ) | ||||||||||||||
21 | : | 9 | = | 2 | remainder ( 3 ) | ||||||||||||||
9 | : | 3 | = | 3 | remainder ( 0 ) | ||||||||||||||
GCD = 3 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.