Question
Find Greatest Common Divisor of 320 and 560, using repeated division.
Answer
The GCD of given numbers is 80.
Explanation
Step 1 : Place the numbers inside division bar:.
| 320 | 560 |
Step 2 : Divide numbers by 2.
| 2 | 320 | 560 |
| 160 | 280 |
Step 3 : Divide numbers by 2.
| 2 | 320 | 560 |
| 2 | 160 | 280 |
| 80 | 140 |
Step 4 : Divide numbers by 2.
| 2 | 320 | 560 |
| 2 | 160 | 280 |
| 2 | 80 | 140 |
| 40 | 70 |
Step 5 : Divide numbers by 2.
| 2 | 320 | 560 |
| 2 | 160 | 280 |
| 2 | 80 | 140 |
| 2 | 40 | 70 |
| 20 | 35 |
Step 6 : Divide numbers by 5.
| 2 | 320 | 560 |
| 2 | 160 | 280 |
| 2 | 80 | 140 |
| 2 | 40 | 70 |
| 5 | 20 | 35 |
| 4 | 7 |
Step 7 : Number 4 and 7, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot2\cdot5 = 80 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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