Find Greatest Common Divisor of 1372 and 948, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 1372 $ by $ 948 $ and get the remainder
The remainder is positive ($ 424 > 0 $), so we will continue with division.
Step 2 :
Divide $ 948 $ by $ \color{blue}{ 424 } $ and get the remainder
The remainder is still positive ($ 100 > 0 $), so we will continue with division.
Step 3 :
Divide $ 424 $ by $ \color{blue}{ 100 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 4 :
Divide $ 100 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
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.
| 1372 | : | 948 | = | 1 | remainder ( 424 ) | ||||||||
| 948 | : | 424 | = | 2 | remainder ( 100 ) | ||||||||
| 424 | : | 100 | = | 4 | remainder ( 24 ) | ||||||||
| 100 | : | 24 | = | 4 | 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.