The GCD of given numbers is 7.
Step 1 :
Divide $ 147 $ by $ 91 $ and get the remainder
The remainder is positive ($ 56 > 0 $), so we will continue with division.
Step 2 :
Divide $ 91 $ by $ \color{blue}{ 56 } $ and get the remainder
The remainder is still positive ($ 35 > 0 $), so we will continue with division.
Step 3 :
Divide $ 56 $ by $ \color{blue}{ 35 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 4 :
Divide $ 35 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 5 :
Divide $ 21 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 6 :
Divide $ 14 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
147 | : | 91 | = | 1 | remainder ( 56 ) | ||||||||||
91 | : | 56 | = | 1 | remainder ( 35 ) | ||||||||||
56 | : | 35 | = | 1 | remainder ( 21 ) | ||||||||||
35 | : | 21 | = | 1 | remainder ( 14 ) | ||||||||||
21 | : | 14 | = | 1 | remainder ( 7 ) | ||||||||||
14 | : | 7 | = | 2 | remainder ( 0 ) | ||||||||||
GCD = 7 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.