Question
Find Greatest Common Divisor of 252 and 432, using repeated division.
Answer
The GCD of given numbers is 36.
Explanation
Step 1 : Place the numbers inside division bar:.
| 252 | 432 |
Step 2 : Divide numbers by 2.
| 2 | 252 | 432 |
| 126 | 216 |
Step 3 : Divide numbers by 2.
| 2 | 252 | 432 |
| 2 | 126 | 216 |
| 63 | 108 |
Step 4 : Divide numbers by 3.
| 2 | 252 | 432 |
| 2 | 126 | 216 |
| 3 | 63 | 108 |
| 21 | 36 |
Step 5 : Divide numbers by 3.
| 2 | 252 | 432 |
| 2 | 126 | 216 |
| 3 | 63 | 108 |
| 3 | 21 | 36 |
| 7 | 12 |
Step 6 : Number 7 and 12, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot3\cdot3 = 36 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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