Question
Find Greatest Common Divisor of 112 and 144, using repeated division.
Answer
The GCD of given numbers is 16.
Explanation
Step 1 : Place the numbers inside division bar:.
| 112 | 144 |
Step 2 : Divide numbers by 2.
| 2 | 112 | 144 |
| 56 | 72 |
Step 3 : Divide numbers by 2.
| 2 | 112 | 144 |
| 2 | 56 | 72 |
| 28 | 36 |
Step 4 : Divide numbers by 2.
| 2 | 112 | 144 |
| 2 | 56 | 72 |
| 2 | 28 | 36 |
| 14 | 18 |
Step 5 : Divide numbers by 2.
| 2 | 112 | 144 |
| 2 | 56 | 72 |
| 2 | 28 | 36 |
| 2 | 14 | 18 |
| 7 | 9 |
Step 6 : Number 7 and 9, cannot be divided any more. The GCD is:
This solution can be visualized using a Venn diagram.
0,0
112
144
2
2
2
2
7
3
3
The GCD equals the product of the numbers at the intersection.
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