Find Greatest Common Divisor of 3915 and 825, using Euclidean algorithm.
Answer
The GCD of given numbers is 15.
Explanation
Step 1 :
Divide $ 3915 $ by $ 825 $ and get the remainder
The remainder is positive ($ 615 > 0 $), so we will continue with division.
Step 2 :
Divide $ 825 $ by $ \color{blue}{ 615 } $ and get the remainder
The remainder is still positive ($ 210 > 0 $), so we will continue with division.
Step 3 :
Divide $ 615 $ by $ \color{blue}{ 210 } $ and get the remainder
The remainder is still positive ($ 195 > 0 $), so we will continue with division.
Step 4 :
Divide $ 210 $ by $ \color{blue}{ 195 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 5 :
Divide $ 195 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 15 }} $.
We can summarize an algorithm into a following table.
| 3915 | : | 825 | = | 4 | remainder ( 615 ) | ||||||||
| 825 | : | 615 | = | 1 | remainder ( 210 ) | ||||||||
| 615 | : | 210 | = | 2 | remainder ( 195 ) | ||||||||
| 210 | : | 195 | = | 1 | remainder ( 15 ) | ||||||||
| 195 | : | 15 | = | 13 | remainder ( 0 ) | ||||||||
| GCD = 15 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.