Find Greatest Common Divisor of 1472 and 1124, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 1472 $ by $ 1124 $ and get the remainder
The remainder is positive ($ 348 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1124 $ by $ \color{blue}{ 348 } $ and get the remainder
The remainder is still positive ($ 80 > 0 $), so we will continue with division.
Step 3 :
Divide $ 348 $ by $ \color{blue}{ 80 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 4 :
Divide $ 80 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 5 :
Divide $ 28 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 24 $ 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.
| 1472 | : | 1124 | = | 1 | remainder ( 348 ) | ||||||||||
| 1124 | : | 348 | = | 3 | remainder ( 80 ) | ||||||||||
| 348 | : | 80 | = | 4 | remainder ( 28 ) | ||||||||||
| 80 | : | 28 | = | 2 | remainder ( 24 ) | ||||||||||
| 28 | : | 24 | = | 1 | remainder ( 4 ) | ||||||||||
| 24 | : | 4 | = | 6 | remainder ( 0 ) | ||||||||||
| GCD = 4 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.