Find Greatest Common Divisor of 24140 and 16762, using Euclidean algorithm.
Answer
The GCD of given numbers is 34.
Explanation
Step 1 :
Divide $ 24140 $ by $ 16762 $ and get the remainder
The remainder is positive ($ 7378 > 0 $), so we will continue with division.
Step 2 :
Divide $ 16762 $ by $ \color{blue}{ 7378 } $ and get the remainder
The remainder is still positive ($ 2006 > 0 $), so we will continue with division.
Step 3 :
Divide $ 7378 $ by $ \color{blue}{ 2006 } $ and get the remainder
The remainder is still positive ($ 1360 > 0 $), so we will continue with division.
Step 4 :
Divide $ 2006 $ by $ \color{blue}{ 1360 } $ and get the remainder
The remainder is still positive ($ 646 > 0 $), so we will continue with division.
Step 5 :
Divide $ 1360 $ by $ \color{blue}{ 646 } $ and get the remainder
The remainder is still positive ($ 68 > 0 $), so we will continue with division.
Step 6 :
Divide $ 646 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 34 > 0 $), so we will continue with division.
Step 7 :
Divide $ 68 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 34 }} $.
We can summarize an algorithm into a following table.
| 24140 | : | 16762 | = | 1 | remainder ( 7378 ) | ||||||||||||
| 16762 | : | 7378 | = | 2 | remainder ( 2006 ) | ||||||||||||
| 7378 | : | 2006 | = | 3 | remainder ( 1360 ) | ||||||||||||
| 2006 | : | 1360 | = | 1 | remainder ( 646 ) | ||||||||||||
| 1360 | : | 646 | = | 2 | remainder ( 68 ) | ||||||||||||
| 646 | : | 68 | = | 9 | remainder ( 34 ) | ||||||||||||
| 68 | : | 34 | = | 2 | remainder ( 0 ) | ||||||||||||
| GCD = 34 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.