Find Greatest Common Divisor of 13572 and 4147, using Euclidean algorithm.
Answer
The GCD of given numbers is 377.
Explanation
Step 1 :
Divide $ 13572 $ by $ 4147 $ and get the remainder
The remainder is positive ($ 1131 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4147 $ by $ \color{blue}{ 1131 } $ and get the remainder
The remainder is still positive ($ 754 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1131 $ by $ \color{blue}{ 754 } $ and get the remainder
The remainder is still positive ($ 377 > 0 $), so we will continue with division.
Step 4 :
Divide $ 754 $ by $ \color{blue}{ 377 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 377 }} $.
We can summarize an algorithm into a following table.
| 13572 | : | 4147 | = | 3 | remainder ( 1131 ) | ||||||
| 4147 | : | 1131 | = | 3 | remainder ( 754 ) | ||||||
| 1131 | : | 754 | = | 1 | remainder ( 377 ) | ||||||
| 754 | : | 377 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 377 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.