Find Greatest Common Divisor of 2520 and 154, using Euclidean algorithm.
Answer
The GCD of given numbers is 14.
Explanation
Step 1 :
Divide $ 2520 $ by $ 154 $ and get the remainder
The remainder is positive ($ 56 > 0 $), so we will continue with division.
Step 2 :
Divide $ 154 $ by $ \color{blue}{ 56 } $ and get the remainder
The remainder is still positive ($ 42 > 0 $), so we will continue with division.
Step 3 :
Divide $ 56 $ by $ \color{blue}{ 42 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 4 :
Divide $ 42 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 14 }} $.
We can summarize an algorithm into a following table.
| 2520 | : | 154 | = | 16 | remainder ( 56 ) | ||||||
| 154 | : | 56 | = | 2 | remainder ( 42 ) | ||||||
| 56 | : | 42 | = | 1 | remainder ( 14 ) | ||||||
| 42 | : | 14 | = | 3 | remainder ( 0 ) | ||||||
| GCD = 14 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.