Find Greatest Common Divisor of 1315 and 572, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 1315 $ by $ 572 $ and get the remainder
The remainder is positive ($ 171 > 0 $), so we will continue with division.
Step 2 :
Divide $ 572 $ by $ \color{blue}{ 171 } $ and get the remainder
The remainder is still positive ($ 59 > 0 $), so we will continue with division.
Step 3 :
Divide $ 171 $ by $ \color{blue}{ 59 } $ and get the remainder
The remainder is still positive ($ 53 > 0 $), so we will continue with division.
Step 4 :
Divide $ 59 $ by $ \color{blue}{ 53 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 5 :
Divide $ 53 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 6 :
Divide $ 6 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
Divide $ 5 $ 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.
| 1315 | : | 572 | = | 2 | remainder ( 171 ) | ||||||||||||
| 572 | : | 171 | = | 3 | remainder ( 59 ) | ||||||||||||
| 171 | : | 59 | = | 2 | remainder ( 53 ) | ||||||||||||
| 59 | : | 53 | = | 1 | remainder ( 6 ) | ||||||||||||
| 53 | : | 6 | = | 8 | remainder ( 5 ) | ||||||||||||
| 6 | : | 5 | = | 1 | remainder ( 1 ) | ||||||||||||
| 5 | : | 1 | = | 5 | remainder ( 0 ) | ||||||||||||
| GCD = 1 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.