Question
Find Greatest Common Divisor of 400 and 600, using repeated division.
Answer
The GCD of given numbers is 40.
Explanation
Step 1 : Place the numbers inside division bar:.
| 400 | 600 |
Step 2 : Divide numbers by 2.
| 2 | 400 | 600 |
| 200 | 300 |
Step 3 : Divide numbers by 2.
| 2 | 400 | 600 |
| 2 | 200 | 300 |
| 100 | 150 |
Step 4 : Divide numbers by 2.
| 2 | 400 | 600 |
| 2 | 200 | 300 |
| 2 | 100 | 150 |
| 50 | 75 |
Step 5 : Divide numbers by 5.
| 2 | 400 | 600 |
| 2 | 200 | 300 |
| 2 | 100 | 150 |
| 5 | 50 | 75 |
| 10 | 15 |
Step 6 : Number 10 and 15, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot5 = 40 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
This page was created using
GCD Calculator