Question
Find Greatest Common Divisor of 2560 and 1440, using repeated division.
Answer
The GCD of given numbers is 160.
Explanation
Step 1 : Place the numbers inside division bar:.
| 2560 | 1440 |
Step 2 : Divide numbers by 2.
| 2 | 2560 | 1440 |
| 1280 | 720 |
Step 3 : Divide numbers by 2.
| 2 | 2560 | 1440 |
| 2 | 1280 | 720 |
| 640 | 360 |
Step 4 : Divide numbers by 2.
| 2 | 2560 | 1440 |
| 2 | 1280 | 720 |
| 2 | 640 | 360 |
| 320 | 180 |
Step 5 : Divide numbers by 2.
| 2 | 2560 | 1440 |
| 2 | 1280 | 720 |
| 2 | 640 | 360 |
| 2 | 320 | 180 |
| 160 | 90 |
Step 6 : Divide numbers by 2.
| 2 | 2560 | 1440 |
| 2 | 1280 | 720 |
| 2 | 640 | 360 |
| 2 | 320 | 180 |
| 2 | 160 | 90 |
| 80 | 45 |
Step 7 : Divide numbers by 5.
| 2 | 2560 | 1440 |
| 2 | 1280 | 720 |
| 2 | 640 | 360 |
| 2 | 320 | 180 |
| 2 | 160 | 90 |
| 5 | 80 | 45 |
| 16 | 9 |
Step 8 : Number 16 and 9, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot2\cdot2\cdot5 = 160 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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