Find Greatest Common Divisor of 5400 and 2412, using Euclidean algorithm.
Answer
The GCD of given numbers is 36.
Explanation
Step 1 :
Divide $ 5400 $ by $ 2412 $ and get the remainder
The remainder is positive ($ 576 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2412 $ by $ \color{blue}{ 576 } $ and get the remainder
The remainder is still positive ($ 108 > 0 $), so we will continue with division.
Step 3 :
Divide $ 576 $ by $ \color{blue}{ 108 } $ and get the remainder
The remainder is still positive ($ 36 > 0 $), so we will continue with division.
Step 4 :
Divide $ 108 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 36 }} $.
We can summarize an algorithm into a following table.
| 5400 | : | 2412 | = | 2 | remainder ( 576 ) | ||||||
| 2412 | : | 576 | = | 4 | remainder ( 108 ) | ||||||
| 576 | : | 108 | = | 5 | remainder ( 36 ) | ||||||
| 108 | : | 36 | = | 3 | remainder ( 0 ) | ||||||
| GCD = 36 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.