Question
Find Greatest Common Divisor of 1400 and 600, using repeated division.
Answer
The GCD of given numbers is 40.
Explanation
Step 1 : Place the numbers inside division bar:.
| 1400 | 600 |
Step 2 : Divide numbers by 2.
| 2 | 1400 | 600 |
| 700 | 300 |
Step 3 : Divide numbers by 2.
| 2 | 1400 | 600 |
| 2 | 700 | 300 |
| 350 | 150 |
Step 4 : Divide numbers by 2.
| 2 | 1400 | 600 |
| 2 | 700 | 300 |
| 2 | 350 | 150 |
| 175 | 75 |
Step 5 : Divide numbers by 5.
| 2 | 1400 | 600 |
| 2 | 700 | 300 |
| 2 | 350 | 150 |
| 5 | 175 | 75 |
| 35 | 15 |
Step 6 : Number 35 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