Find Greatest Common Divisor of 33 and 150, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 150 $ by $ 33 $ and get the remainder
The remainder is positive ($ 18 > 0 $), so we will continue with division.
Step 2 :
Divide $ 33 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 3 :
Divide $ 18 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 4 :
Divide $ 15 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
| 150 | : | 33 | = | 4 | remainder ( 18 ) | ||||||
| 33 | : | 18 | = | 1 | remainder ( 15 ) | ||||||
| 18 | : | 15 | = | 1 | remainder ( 3 ) | ||||||
| 15 | : | 3 | = | 5 | remainder ( 0 ) | ||||||
| GCD = 3 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.