Question
Find Greatest Common Divisor of 80 and 144, using repeated division.
Answer
The GCD of given numbers is 16.
Explanation
Step 1 : Place the numbers inside division bar:.
| 80 | 144 |
Step 2 : Divide numbers by 2.
| 2 | 80 | 144 |
| 40 | 72 |
Step 3 : Divide numbers by 2.
| 2 | 80 | 144 |
| 2 | 40 | 72 |
| 20 | 36 |
Step 4 : Divide numbers by 2.
| 2 | 80 | 144 |
| 2 | 40 | 72 |
| 2 | 20 | 36 |
| 10 | 18 |
Step 5 : Divide numbers by 2.
| 2 | 80 | 144 |
| 2 | 40 | 72 |
| 2 | 20 | 36 |
| 2 | 10 | 18 |
| 5 | 9 |
Step 6 : Number 5 and 9, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot2 = 16 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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