Find Greatest Common Divisor of 192 and 264, using Euclidean algorithm.
Answer
The GCD of given numbers is 24.
Explanation
Step 1 :
Divide $ 264 $ by $ 192 $ and get the remainder
The remainder is positive ($ 72 > 0 $), so we will continue with division.
Step 2 :
Divide $ 192 $ by $ \color{blue}{ 72 } $ and get the remainder
The remainder is still positive ($ 48 > 0 $), so we will continue with division.
Step 3 :
Divide $ 72 $ by $ \color{blue}{ 48 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 4 :
Divide $ 48 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 24 }} $.
We can summarize an algorithm into a following table.
| 264 | : | 192 | = | 1 | remainder ( 72 ) | ||||||
| 192 | : | 72 | = | 2 | remainder ( 48 ) | ||||||
| 72 | : | 48 | = | 1 | remainder ( 24 ) | ||||||
| 48 | : | 24 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 24 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.