Find Greatest Common Divisor of 235 and 1260, using Euclidean algorithm.
Answer
The GCD of given numbers is 5.
Explanation
Step 1 :
Divide $ 1260 $ by $ 235 $ and get the remainder
The remainder is positive ($ 85 > 0 $), so we will continue with division.
Step 2 :
Divide $ 235 $ by $ \color{blue}{ 85 } $ and get the remainder
The remainder is still positive ($ 65 > 0 $), so we will continue with division.
Step 3 :
Divide $ 85 $ by $ \color{blue}{ 65 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 4 :
Divide $ 65 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 5 :
Divide $ 20 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 5 }} $.
We can summarize an algorithm into a following table.
| 1260 | : | 235 | = | 5 | remainder ( 85 ) | ||||||||
| 235 | : | 85 | = | 2 | remainder ( 65 ) | ||||||||
| 85 | : | 65 | = | 1 | remainder ( 20 ) | ||||||||
| 65 | : | 20 | = | 3 | remainder ( 5 ) | ||||||||
| 20 | : | 5 | = | 4 | remainder ( 0 ) | ||||||||
| GCD = 5 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.