Find Greatest Common Divisor of 1632 and 1187, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 1632 $ by $ 1187 $ and get the remainder
The remainder is positive ($ 445 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1187 $ by $ \color{blue}{ 445 } $ and get the remainder
The remainder is still positive ($ 297 > 0 $), so we will continue with division.
Step 3 :
Divide $ 445 $ by $ \color{blue}{ 297 } $ and get the remainder
The remainder is still positive ($ 148 > 0 $), so we will continue with division.
Step 4 :
Divide $ 297 $ by $ \color{blue}{ 148 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 148 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
| 1632 | : | 1187 | = | 1 | remainder ( 445 ) | ||||||||
| 1187 | : | 445 | = | 2 | remainder ( 297 ) | ||||||||
| 445 | : | 297 | = | 1 | remainder ( 148 ) | ||||||||
| 297 | : | 148 | = | 2 | remainder ( 1 ) | ||||||||
| 148 | : | 1 | = | 148 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.