Find Greatest Common Divisor of 14973 and 4746, using Euclidean algorithm.
Answer
The GCD of given numbers is 21.
Explanation
Step 1 :
Divide $ 14973 $ by $ 4746 $ and get the remainder
The remainder is positive ($ 735 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4746 $ by $ \color{blue}{ 735 } $ and get the remainder
The remainder is still positive ($ 336 > 0 $), so we will continue with division.
Step 3 :
Divide $ 735 $ by $ \color{blue}{ 336 } $ and get the remainder
The remainder is still positive ($ 63 > 0 $), so we will continue with division.
Step 4 :
Divide $ 336 $ by $ \color{blue}{ 63 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 5 :
Divide $ 63 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 21 }} $.
We can summarize an algorithm into a following table.
| 14973 | : | 4746 | = | 3 | remainder ( 735 ) | ||||||||
| 4746 | : | 735 | = | 6 | remainder ( 336 ) | ||||||||
| 735 | : | 336 | = | 2 | remainder ( 63 ) | ||||||||
| 336 | : | 63 | = | 5 | remainder ( 21 ) | ||||||||
| 63 | : | 21 | = | 3 | remainder ( 0 ) | ||||||||
| GCD = 21 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.