Find Greatest Common Divisor of 70 and 120, using Euclidean algorithm.
Answer
The GCD of given numbers is 10.
Explanation
Step 1 :
Divide $ 120 $ by $ 70 $ and get the remainder
The remainder is positive ($ 50 > 0 $), so we will continue with division.
Step 2 :
Divide $ 70 $ by $ \color{blue}{ 50 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 3 :
Divide $ 50 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 4 :
Divide $ 20 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.
We can summarize an algorithm into a following table.
| 120 | : | 70 | = | 1 | remainder ( 50 ) | ||||||
| 70 | : | 50 | = | 1 | remainder ( 20 ) | ||||||
| 50 | : | 20 | = | 2 | remainder ( 10 ) | ||||||
| 20 | : | 10 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 10 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.