Question
Find Greatest Common Divisor of 32, 8 and 56, using repeated division.
Answer
The GCD of given numbers is 8.
Explanation
Step 1 : Place the numbers inside division bar:.
| 32 | 8 | 56 |
Step 2 : Divide numbers by 2.
| 2 | 32 | 8 | 56 |
| 16 | 4 | 28 |
Step 3 : Divide numbers by 2.
| 2 | 32 | 8 | 56 |
| 2 | 16 | 4 | 28 |
| 8 | 2 | 14 |
Step 4 : Divide numbers by 2.
| 2 | 32 | 8 | 56 |
| 2 | 16 | 4 | 28 |
| 2 | 8 | 2 | 14 |
| 4 | 1 | 7 |
Step 5 : Number 4, 1 and 7, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2 = 8 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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