Find Greatest Common Divisor of 14560 and 8250, using Euclidean algorithm.
Answer
The GCD of given numbers is 10.
Explanation
Step 1 :
Divide $ 14560 $ by $ 8250 $ and get the remainder
The remainder is positive ($ 6310 > 0 $), so we will continue with division.
Step 2 :
Divide $ 8250 $ by $ \color{blue}{ 6310 } $ and get the remainder
The remainder is still positive ($ 1940 > 0 $), so we will continue with division.
Step 3 :
Divide $ 6310 $ by $ \color{blue}{ 1940 } $ and get the remainder
The remainder is still positive ($ 490 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1940 $ by $ \color{blue}{ 490 } $ and get the remainder
The remainder is still positive ($ 470 > 0 $), so we will continue with division.
Step 5 :
Divide $ 490 $ by $ \color{blue}{ 470 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 6 :
Divide $ 470 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 7 :
Divide $ 20 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.
We can summarize an algorithm into a following table.
| 14560 | : | 8250 | = | 1 | remainder ( 6310 ) | ||||||||||||
| 8250 | : | 6310 | = | 1 | remainder ( 1940 ) | ||||||||||||
| 6310 | : | 1940 | = | 3 | remainder ( 490 ) | ||||||||||||
| 1940 | : | 490 | = | 3 | remainder ( 470 ) | ||||||||||||
| 490 | : | 470 | = | 1 | remainder ( 20 ) | ||||||||||||
| 470 | : | 20 | = | 23 | remainder ( 10 ) | ||||||||||||
| 20 | : | 10 | = | 2 | remainder ( 0 ) | ||||||||||||
| GCD = 10 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.