Find Greatest Common Divisor of 6773760 and 12902400, using Euclidean algorithm.
Answer
The GCD of given numbers is 322560.
Explanation
Step 1 :
Divide $ 12902400 $ by $ 6773760 $ and get the remainder
The remainder is positive ($ 6128640 > 0 $), so we will continue with division.
Step 2 :
Divide $ 6773760 $ by $ \color{blue}{ 6128640 } $ and get the remainder
The remainder is still positive ($ 645120 > 0 $), so we will continue with division.
Step 3 :
Divide $ 6128640 $ by $ \color{blue}{ 645120 } $ and get the remainder
The remainder is still positive ($ 322560 > 0 $), so we will continue with division.
Step 4 :
Divide $ 645120 $ by $ \color{blue}{ 322560 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 322560 }} $.
We can summarize an algorithm into a following table.
| 12902400 | : | 6773760 | = | 1 | remainder ( 6128640 ) | ||||||
| 6773760 | : | 6128640 | = | 1 | remainder ( 645120 ) | ||||||
| 6128640 | : | 645120 | = | 9 | remainder ( 322560 ) | ||||||
| 645120 | : | 322560 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 322560 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.