Find Greatest Common Divisor of 93149832 and 73482, using Euclidean algorithm.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 :
Divide $ 93149832 $ by $ 73482 $ and get the remainder
The remainder is positive ($ 48138 > 0 $), so we will continue with division.
Step 2 :
Divide $ 73482 $ by $ \color{blue}{ 48138 } $ and get the remainder
The remainder is still positive ($ 25344 > 0 $), so we will continue with division.
Step 3 :
Divide $ 48138 $ by $ \color{blue}{ 25344 } $ and get the remainder
The remainder is still positive ($ 22794 > 0 $), so we will continue with division.
Step 4 :
Divide $ 25344 $ by $ \color{blue}{ 22794 } $ and get the remainder
The remainder is still positive ($ 2550 > 0 $), so we will continue with division.
Step 5 :
Divide $ 22794 $ by $ \color{blue}{ 2550 } $ and get the remainder
The remainder is still positive ($ 2394 > 0 $), so we will continue with division.
Step 6 :
Divide $ 2550 $ by $ \color{blue}{ 2394 } $ and get the remainder
The remainder is still positive ($ 156 > 0 $), so we will continue with division.
Step 7 :
Divide $ 2394 $ by $ \color{blue}{ 156 } $ and get the remainder
The remainder is still positive ($ 54 > 0 $), so we will continue with division.
Step 8 :
Divide $ 156 $ by $ \color{blue}{ 54 } $ and get the remainder
The remainder is still positive ($ 48 > 0 $), so we will continue with division.
Step 9 :
Divide $ 54 $ by $ \color{blue}{ 48 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 10 :
Divide $ 48 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.
We can summarize an algorithm into a following table.
| 93149832 | : | 73482 | = | 1267 | remainder ( 48138 ) | ||||||||||||||||||
| 73482 | : | 48138 | = | 1 | remainder ( 25344 ) | ||||||||||||||||||
| 48138 | : | 25344 | = | 1 | remainder ( 22794 ) | ||||||||||||||||||
| 25344 | : | 22794 | = | 1 | remainder ( 2550 ) | ||||||||||||||||||
| 22794 | : | 2550 | = | 8 | remainder ( 2394 ) | ||||||||||||||||||
| 2550 | : | 2394 | = | 1 | remainder ( 156 ) | ||||||||||||||||||
| 2394 | : | 156 | = | 15 | remainder ( 54 ) | ||||||||||||||||||
| 156 | : | 54 | = | 2 | remainder ( 48 ) | ||||||||||||||||||
| 54 | : | 48 | = | 1 | remainder ( 6 ) | ||||||||||||||||||
| 48 | : | 6 | = | 8 | remainder ( 0 ) | ||||||||||||||||||
| GCD = 6 | |||||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.