Find Greatest Common Divisor of 792 and 275, using Euclidean algorithm.
Answer
The GCD of given numbers is 11.
Explanation
Step 1 :
Divide $ 792 $ by $ 275 $ and get the remainder
The remainder is positive ($ 242 > 0 $), so we will continue with division.
Step 2 :
Divide $ 275 $ by $ \color{blue}{ 242 } $ and get the remainder
The remainder is still positive ($ 33 > 0 $), so we will continue with division.
Step 3 :
Divide $ 242 $ by $ \color{blue}{ 33 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 4 :
Divide $ 33 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.
We can summarize an algorithm into a following table.
| 792 | : | 275 | = | 2 | remainder ( 242 ) | ||||||
| 275 | : | 242 | = | 1 | remainder ( 33 ) | ||||||
| 242 | : | 33 | = | 7 | remainder ( 11 ) | ||||||
| 33 | : | 11 | = | 3 | remainder ( 0 ) | ||||||
| GCD = 11 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.