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Question
Find the smallest number by which 2592 be multiplied so that the product is a perfect square.
Solution
2592 = `bar(2xx2) xx bar(2xx2) xx 2 xx bar(3xx3) xx bar(3xx3)`
On grouping the prime factors of 2592 as shown; on factor i.e. 2 is left which cannot be paired with equal factor.
| 2 | 2592 |
| 2 | 1296 |
| 2 | 648 |
| 2 | 324 |
| 2 | 162 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
2 is the smallest number that must be multiplied by 2592 to get a perfect square.
2592 × 2 = 5184.
The prime factorization of 5184 is:
5184 = 26.34
Both powers (6 and 4) are even, so 5184 is a perfect square.
The smallest number is 2.
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