Find Greatest Common Divisor of 48 and 30, using Euclidean algorithm.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 :
Divide $ 48 $ by $ 30 $ and get the remainder
The remainder is positive ($ 18 > 0 $), so we will continue with division.
Step 2 :
Divide $ 30 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 3 :
Divide $ 18 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 12 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.
We can summarize an algorithm into a following table.
| 48 | : | 30 | = | 1 | remainder ( 18 ) | ||||||
| 30 | : | 18 | = | 1 | remainder ( 12 ) | ||||||
| 18 | : | 12 | = | 1 | remainder ( 6 ) | ||||||
| 12 | : | 6 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 6 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.