Find Greatest Common Divisor of 2600 and 5500, using Euclidean algorithm.
Answer
The GCD of given numbers is 100.
Explanation
Step 1 :
Divide $ 5500 $ by $ 2600 $ and get the remainder
The remainder is positive ($ 300 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2600 $ by $ \color{blue}{ 300 } $ and get the remainder
The remainder is still positive ($ 200 > 0 $), so we will continue with division.
Step 3 :
Divide $ 300 $ by $ \color{blue}{ 200 } $ and get the remainder
The remainder is still positive ($ 100 > 0 $), so we will continue with division.
Step 4 :
Divide $ 200 $ by $ \color{blue}{ 100 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 100 }} $.
We can summarize an algorithm into a following table.
| 5500 | : | 2600 | = | 2 | remainder ( 300 ) | ||||||
| 2600 | : | 300 | = | 8 | remainder ( 200 ) | ||||||
| 300 | : | 200 | = | 1 | remainder ( 100 ) | ||||||
| 200 | : | 100 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 100 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.