Question
Find Greatest Common Divisor of 168 and 504, using repeated division.
Answer
The GCD of given numbers is 168.
Explanation
Step 1 : Place the numbers inside division bar:.
| 168 | 504 |
Step 2 : Divide numbers by 2.
| 2 | 168 | 504 |
| 84 | 252 |
Step 3 : Divide numbers by 2.
| 2 | 168 | 504 |
| 2 | 84 | 252 |
| 42 | 126 |
Step 4 : Divide numbers by 2.
| 2 | 168 | 504 |
| 2 | 84 | 252 |
| 2 | 42 | 126 |
| 21 | 63 |
Step 5 : Divide numbers by 3.
| 2 | 168 | 504 |
| 2 | 84 | 252 |
| 2 | 42 | 126 |
| 3 | 21 | 63 |
| 7 | 21 |
Step 6 : Divide numbers by 7.
| 2 | 168 | 504 |
| 2 | 84 | 252 |
| 2 | 42 | 126 |
| 3 | 21 | 63 |
| 7 | 7 | 21 |
| 1 | 3 |
Step 7 : Number 1 and 3, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot3\cdot7 = 168 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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