Find Greatest Common Divisor of 20, 40 and 80, using repeated division.
Answer
The GCD of given numbers is 20.
Explanation
Step 1 : Place the numbers inside division bar:.
| 20 | 40 | 80 |
Step 2 : Divide numbers by 2.
| 2 | 20 | 40 | 80 |
| 10 | 20 | 40 |
Step 3 : Divide numbers by 2.
| 2 | 20 | 40 | 80 |
| 2 | 10 | 20 | 40 |
| 5 | 10 | 20 |
Step 4 : Divide numbers by 5.
| 2 | 20 | 40 | 80 |
| 2 | 10 | 20 | 40 |
| 5 | 5 | 10 | 20 |
| 1 | 2 | 4 |
Step 5 : Number 1, 2 and 4, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot5 = 20 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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