Find Greatest Common Divisor of 2516 and 1125, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 2516 $ by $ 1125 $ and get the remainder
The remainder is positive ($ 266 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1125 $ by $ \color{blue}{ 266 } $ and get the remainder
The remainder is still positive ($ 61 > 0 $), so we will continue with division.
Step 3 :
Divide $ 266 $ by $ \color{blue}{ 61 } $ and get the remainder
The remainder is still positive ($ 22 > 0 $), so we will continue with division.
Step 4 :
Divide $ 61 $ by $ \color{blue}{ 22 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 5 :
Divide $ 22 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 6 :
Divide $ 17 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 5 $ 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.
| 2516 | : | 1125 | = | 2 | remainder ( 266 ) | ||||||||||||||
| 1125 | : | 266 | = | 4 | remainder ( 61 ) | ||||||||||||||
| 266 | : | 61 | = | 4 | remainder ( 22 ) | ||||||||||||||
| 61 | : | 22 | = | 2 | remainder ( 17 ) | ||||||||||||||
| 22 | : | 17 | = | 1 | remainder ( 5 ) | ||||||||||||||
| 17 | : | 5 | = | 3 | remainder ( 2 ) | ||||||||||||||
| 5 | : | 2 | = | 2 | 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.