Find Greatest Common Divisor of 1147 and 899, using Euclidean algorithm.
Answer
The GCD of given numbers is 31.
Explanation
Step 1 :
Divide $ 1147 $ by $ 899 $ and get the remainder
The remainder is positive ($ 248 > 0 $), so we will continue with division.
Step 2 :
Divide $ 899 $ by $ \color{blue}{ 248 } $ and get the remainder
The remainder is still positive ($ 155 > 0 $), so we will continue with division.
Step 3 :
Divide $ 248 $ by $ \color{blue}{ 155 } $ and get the remainder
The remainder is still positive ($ 93 > 0 $), so we will continue with division.
Step 4 :
Divide $ 155 $ by $ \color{blue}{ 93 } $ and get the remainder
The remainder is still positive ($ 62 > 0 $), so we will continue with division.
Step 5 :
Divide $ 93 $ by $ \color{blue}{ 62 } $ and get the remainder
The remainder is still positive ($ 31 > 0 $), so we will continue with division.
Step 6 :
Divide $ 62 $ by $ \color{blue}{ 31 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 31 }} $.
We can summarize an algorithm into a following table.
| 1147 | : | 899 | = | 1 | remainder ( 248 ) | ||||||||||
| 899 | : | 248 | = | 3 | remainder ( 155 ) | ||||||||||
| 248 | : | 155 | = | 1 | remainder ( 93 ) | ||||||||||
| 155 | : | 93 | = | 1 | remainder ( 62 ) | ||||||||||
| 93 | : | 62 | = | 1 | remainder ( 31 ) | ||||||||||
| 62 | : | 31 | = | 2 | remainder ( 0 ) | ||||||||||
| GCD = 31 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.