Find Greatest Common Divisor of 14860 and 4424, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 14860 $ by $ 4424 $ and get the remainder
The remainder is positive ($ 1588 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4424 $ by $ \color{blue}{ 1588 } $ and get the remainder
The remainder is still positive ($ 1248 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1588 $ by $ \color{blue}{ 1248 } $ and get the remainder
The remainder is still positive ($ 340 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1248 $ by $ \color{blue}{ 340 } $ and get the remainder
The remainder is still positive ($ 228 > 0 $), so we will continue with division.
Step 5 :
Divide $ 340 $ by $ \color{blue}{ 228 } $ and get the remainder
The remainder is still positive ($ 112 > 0 $), so we will continue with division.
Step 6 :
Divide $ 228 $ by $ \color{blue}{ 112 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 7 :
Divide $ 112 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 14860 | : | 4424 | = | 3 | remainder ( 1588 ) | ||||||||||||
| 4424 | : | 1588 | = | 2 | remainder ( 1248 ) | ||||||||||||
| 1588 | : | 1248 | = | 1 | remainder ( 340 ) | ||||||||||||
| 1248 | : | 340 | = | 3 | remainder ( 228 ) | ||||||||||||
| 340 | : | 228 | = | 1 | remainder ( 112 ) | ||||||||||||
| 228 | : | 112 | = | 2 | remainder ( 4 ) | ||||||||||||
| 112 | : | 4 | = | 28 | remainder ( 0 ) | ||||||||||||
| GCD = 4 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.