Question
Find Greatest Common Divisor of 42 and 77, using Euclidean algorithm.
Answer
The GCD of given numbers is 7.
Explanation
Step 1 :
Divide by and get the remainder
The remainder is positive (), so we will continue with division.
Step 2 :
Divide by and get the remainder
The remainder is still positive (), so we will continue with division.
Step 3 :
Divide by and get the remainder
The remainder is zero => GCD is the last divisor .
We can summarize an algorithm into a following table.
| 77 | : | 42 | = | 1 | remainder ( 35 ) | ||||
| 42 | : | 35 | = | 1 | remainder ( 7 ) | ||||
| 35 | : | 7 | = | 5 | remainder ( 0 ) | ||||
| GCD = 7 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
42
77
7
2
3
11
The GCD equals the product of the numbers at the intersection.
This page was created using
GCD Calculator