The GCD of given numbers is 21.
Step 1 :
Divide $ 462 $ by $ 357 $ and get the remainder
The remainder is positive ($ 105 > 0 $), so we will continue with division.
Step 2 :
Divide $ 357 $ by $ \color{blue}{ 105 } $ and get the remainder
The remainder is still positive ($ 42 > 0 $), so we will continue with division.
Step 3 :
Divide $ 105 $ by $ \color{blue}{ 42 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 4 :
Divide $ 42 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 21 }} $.
We can summarize an algorithm into a following table.
462 | : | 357 | = | 1 | remainder ( 105 ) | ||||||
357 | : | 105 | = | 3 | remainder ( 42 ) | ||||||
105 | : | 42 | = | 2 | remainder ( 21 ) | ||||||
42 | : | 21 | = | 2 | remainder ( 0 ) | ||||||
GCD = 21 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.