By which smallest number 1323 must be multiplied so that it becomes a perfect cube
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Answer:
The smallest number is 7.
Step-by-step explanation:
To find the ‘smallest number’ by which 1323 will be multiplied, we need to factorize 1323 as under:
1323 = 3 x 441
1323 = 3 x 3 x 147
1323 = 3 x 3 x 3 x 49
1323 = 3 x 3 x 3 x 7 x 7
The above can be written as 1323 = 3^3 x 7^2
Now, 7 is not in triplet. If 7 is in triplet, then derived number will be perfect cube.
Hence, 1323 must be ‘multiplied by 7’ to get a ‘perfect cube’ as shown below:
1323 = 3^3 x 7^3 = 21 x 21 x 21 = 9261.
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