The GCD of given numbers is 11.
Step 1 :
Divide $ 374 $ by $ 143 $ and get the remainder
The remainder is positive ($ 88 > 0 $), so we will continue with division.
Step 2 :
Divide $ 143 $ by $ \color{blue}{ 88 } $ and get the remainder
The remainder is still positive ($ 55 > 0 $), so we will continue with division.
Step 3 :
Divide $ 88 $ by $ \color{blue}{ 55 } $ and get the remainder
The remainder is still positive ($ 33 > 0 $), so we will continue with division.
Step 4 :
Divide $ 55 $ by $ \color{blue}{ 33 } $ and get the remainder
The remainder is still positive ($ 22 > 0 $), so we will continue with division.
Step 5 :
Divide $ 33 $ by $ \color{blue}{ 22 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 6 :
Divide $ 22 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.
We can summarize an algorithm into a following table.
374 | : | 143 | = | 2 | remainder ( 88 ) | ||||||||||
143 | : | 88 | = | 1 | remainder ( 55 ) | ||||||||||
88 | : | 55 | = | 1 | remainder ( 33 ) | ||||||||||
55 | : | 33 | = | 1 | remainder ( 22 ) | ||||||||||
33 | : | 22 | = | 1 | remainder ( 11 ) | ||||||||||
22 | : | 11 | = | 2 | remainder ( 0 ) | ||||||||||
GCD = 11 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.