Find Greatest Common Divisor of 2560 and 1440, using Euclidean algorithm.
Answer
The GCD of given numbers is 160.
Explanation
Step 1 :
Divide $ 2560 $ by $ 1440 $ and get the remainder
The remainder is positive ($ 1120 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1440 $ by $ \color{blue}{ 1120 } $ and get the remainder
The remainder is still positive ($ 320 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1120 $ by $ \color{blue}{ 320 } $ and get the remainder
The remainder is still positive ($ 160 > 0 $), so we will continue with division.
Step 4 :
Divide $ 320 $ by $ \color{blue}{ 160 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 160 }} $.
We can summarize an algorithm into a following table.
| 2560 | : | 1440 | = | 1 | remainder ( 1120 ) | ||||||
| 1440 | : | 1120 | = | 1 | remainder ( 320 ) | ||||||
| 1120 | : | 320 | = | 3 | remainder ( 160 ) | ||||||
| 320 | : | 160 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 160 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.