Find Greatest Common Divisor of 1028 and 576, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 1028 $ by $ 576 $ and get the remainder
The remainder is positive ($ 452 > 0 $), so we will continue with division.
Step 2 :
Divide $ 576 $ by $ \color{blue}{ 452 } $ and get the remainder
The remainder is still positive ($ 124 > 0 $), so we will continue with division.
Step 3 :
Divide $ 452 $ by $ \color{blue}{ 124 } $ and get the remainder
The remainder is still positive ($ 80 > 0 $), so we will continue with division.
Step 4 :
Divide $ 124 $ by $ \color{blue}{ 80 } $ and get the remainder
The remainder is still positive ($ 44 > 0 $), so we will continue with division.
Step 5 :
Divide $ 80 $ by $ \color{blue}{ 44 } $ and get the remainder
The remainder is still positive ($ 36 > 0 $), so we will continue with division.
Step 6 :
Divide $ 44 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 7 :
Divide $ 36 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 8 :
Divide $ 8 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 1028 | : | 576 | = | 1 | remainder ( 452 ) | ||||||||||||||
| 576 | : | 452 | = | 1 | remainder ( 124 ) | ||||||||||||||
| 452 | : | 124 | = | 3 | remainder ( 80 ) | ||||||||||||||
| 124 | : | 80 | = | 1 | remainder ( 44 ) | ||||||||||||||
| 80 | : | 44 | = | 1 | remainder ( 36 ) | ||||||||||||||
| 44 | : | 36 | = | 1 | remainder ( 8 ) | ||||||||||||||
| 36 | : | 8 | = | 4 | remainder ( 4 ) | ||||||||||||||
| 8 | : | 4 | = | 2 | remainder ( 0 ) | ||||||||||||||
| GCD = 4 | |||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.