Find Greatest Common Divisor of 24 and 48, using repeated division.
Answer
The GCD of given numbers is 24.
Explanation
Step 1 : Place the numbers inside division bar:.
| 24 | 48 |
Step 2 : Divide numbers by 2.
| 2 | 24 | 48 |
| 12 | 24 |
Step 3 : Divide numbers by 2.
| 2 | 24 | 48 |
| 2 | 12 | 24 |
| 6 | 12 |
Step 4 : Divide numbers by 2.
| 2 | 24 | 48 |
| 2 | 12 | 24 |
| 2 | 6 | 12 |
| 3 | 6 |
Step 5 : Divide numbers by 3.
| 2 | 24 | 48 |
| 2 | 12 | 24 |
| 2 | 6 | 12 |
| 3 | 3 | 6 |
| 1 | 2 |
Step 6 : Number 1 and 2, 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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