Find Greatest Common Divisor of 1529 and 1039, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 1529 $ by $ 1039 $ and get the remainder
The remainder is positive ($ 490 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1039 $ by $ \color{blue}{ 490 } $ and get the remainder
The remainder is still positive ($ 59 > 0 $), so we will continue with division.
Step 3 :
Divide $ 490 $ by $ \color{blue}{ 59 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 4 :
Divide $ 59 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 5 :
Divide $ 18 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 6 :
Divide $ 5 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
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.
| 1529 | : | 1039 | = | 1 | remainder ( 490 ) | ||||||||||||||
| 1039 | : | 490 | = | 2 | remainder ( 59 ) | ||||||||||||||
| 490 | : | 59 | = | 8 | remainder ( 18 ) | ||||||||||||||
| 59 | : | 18 | = | 3 | remainder ( 5 ) | ||||||||||||||
| 18 | : | 5 | = | 3 | remainder ( 3 ) | ||||||||||||||
| 5 | : | 3 | = | 1 | 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.