Find Greatest Common Divisor of 7250 and 2360, using Euclidean algorithm.
Answer
The GCD of given numbers is 10.
Explanation
Step 1 :
Divide $ 7250 $ by $ 2360 $ and get the remainder
The remainder is positive ($ 170 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2360 $ by $ \color{blue}{ 170 } $ and get the remainder
The remainder is still positive ($ 150 > 0 $), so we will continue with division.
Step 3 :
Divide $ 170 $ by $ \color{blue}{ 150 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 4 :
Divide $ 150 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 5 :
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.
| 7250 | : | 2360 | = | 3 | remainder ( 170 ) | ||||||||
| 2360 | : | 170 | = | 13 | remainder ( 150 ) | ||||||||
| 170 | : | 150 | = | 1 | remainder ( 20 ) | ||||||||
| 150 | : | 20 | = | 7 | 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.