Question
Find Greatest Common Divisor of 360 and 504, using repeated division.
Answer
The GCD of given numbers is 72.
Explanation
Step 1 : Place the numbers inside division bar:.
| 360 | 504 |
Step 2 : Divide numbers by 2.
| 2 | 360 | 504 |
| 180 | 252 |
Step 3 : Divide numbers by 2.
| 2 | 360 | 504 |
| 2 | 180 | 252 |
| 90 | 126 |
Step 4 : Divide numbers by 2.
| 2 | 360 | 504 |
| 2 | 180 | 252 |
| 2 | 90 | 126 |
| 45 | 63 |
Step 5 : Divide numbers by 3.
| 2 | 360 | 504 |
| 2 | 180 | 252 |
| 2 | 90 | 126 |
| 3 | 45 | 63 |
| 15 | 21 |
Step 6 : Divide numbers by 3.
| 2 | 360 | 504 |
| 2 | 180 | 252 |
| 2 | 90 | 126 |
| 3 | 45 | 63 |
| 3 | 15 | 21 |
| 5 | 7 |
Step 7 : Number 5 and 7, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot3\cdot3 = 72 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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