Find Greatest Common Divisor of 24 and 69, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 69 $ by $ 24 $ and get the remainder
The remainder is positive ($ 21 > 0 $), so we will continue with division.
Step 2 :
Divide $ 24 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 3 :
Divide $ 21 $ 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.
| 69 | : | 24 | = | 2 | remainder ( 21 ) | ||||
| 24 | : | 21 | = | 1 | remainder ( 3 ) | ||||
| 21 | : | 3 | = | 7 | remainder ( 0 ) | ||||
| GCD = 3 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
This page was created using
GCD Calculator