Question
Find Greatest Common Divisor of 2024 and 1058, using Euclidean algorithm.
Answer
The GCD of given numbers is 46.
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 still positive (), so we will continue with division.
Step 4 :
Divide by and get the remainder
The remainder is zero => GCD is the last divisor .
We can summarize an algorithm into a following table.
| 2024 | : | 1058 | = | 1 | remainder ( 966 ) | ||||||
| 1058 | : | 966 | = | 1 | remainder ( 92 ) | ||||||
| 966 | : | 92 | = | 10 | remainder ( 46 ) | ||||||
| 92 | : | 46 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 46 | |||||||||||
This solution can be visualized using a Venn diagram.
0,0
2024
1058
2
23
2
2
11
23
The GCD equals the product of the numbers at the intersection.
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