Find Greatest Common Divisor of 104 and 64, using Euclidean algorithm.
Answer
The GCD of given numbers is 8.
Explanation
Step 1 :
Divide $ 104 $ by $ 64 $ and get the remainder
The remainder is positive ($ 40 > 0 $), so we will continue with division.
Step 2 :
Divide $ 64 $ by $ \color{blue}{ 40 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 3 :
Divide $ 40 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 4 :
Divide $ 24 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 16 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.
We can summarize an algorithm into a following table.
| 104 | : | 64 | = | 1 | remainder ( 40 ) | ||||||||
| 64 | : | 40 | = | 1 | remainder ( 24 ) | ||||||||
| 40 | : | 24 | = | 1 | remainder ( 16 ) | ||||||||
| 24 | : | 16 | = | 1 | remainder ( 8 ) | ||||||||
| 16 | : | 8 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 8 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.