Find Greatest Common Divisor of 72, 120 and 144, using repeated division.
Answer
The GCD of given numbers is 24.
Explanation
Step 1 : Place the numbers inside division bar:.
| 72 | 120 | 144 |
Step 2 : Divide numbers by 2.
| 2 | 72 | 120 | 144 |
| 36 | 60 | 72 |
Step 3 : Divide numbers by 2.
| 2 | 72 | 120 | 144 |
| 2 | 36 | 60 | 72 |
| 18 | 30 | 36 |
Step 4 : Divide numbers by 2.
| 2 | 72 | 120 | 144 |
| 2 | 36 | 60 | 72 |
| 2 | 18 | 30 | 36 |
| 9 | 15 | 18 |
Step 5 : Divide numbers by 3.
| 2 | 72 | 120 | 144 |
| 2 | 36 | 60 | 72 |
| 2 | 18 | 30 | 36 |
| 3 | 9 | 15 | 18 |
| 3 | 5 | 6 |
Step 6 : Number 3, 5 and 6, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot3 = 24 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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