Find Greatest Common Divisor of 1716 and 1260, using Euclidean algorithm.
Answer
The GCD of given numbers is 12.
Explanation
Step 1 :
Divide $ 1716 $ by $ 1260 $ and get the remainder
The remainder is positive ($ 456 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1260 $ by $ \color{blue}{ 456 } $ and get the remainder
The remainder is still positive ($ 348 > 0 $), so we will continue with division.
Step 3 :
Divide $ 456 $ by $ \color{blue}{ 348 } $ and get the remainder
The remainder is still positive ($ 108 > 0 $), so we will continue with division.
Step 4 :
Divide $ 348 $ by $ \color{blue}{ 108 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 5 :
Divide $ 108 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 6 :
Divide $ 24 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 12 }} $.
We can summarize an algorithm into a following table.
| 1716 | : | 1260 | = | 1 | remainder ( 456 ) | ||||||||||
| 1260 | : | 456 | = | 2 | remainder ( 348 ) | ||||||||||
| 456 | : | 348 | = | 1 | remainder ( 108 ) | ||||||||||
| 348 | : | 108 | = | 3 | remainder ( 24 ) | ||||||||||
| 108 | : | 24 | = | 4 | remainder ( 12 ) | ||||||||||
| 24 | : | 12 | = | 2 | remainder ( 0 ) | ||||||||||
| GCD = 12 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.