Question
Download Solution PDFWhat is the smallest number which, when multiplied by 5673375, yields a perfect cube?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula Used:
A perfect cube has prime factors with exponents that are multiples of 3.
Calculation:
The prime factorization of 5673375 = 53 × 33 × 412.
To make this a perfect cube, the exponent of each prime factor must be a multiple of 3.
The prime factors and their current exponents are:
3: exponent 3 (already a multiple of 3)
5: exponent 3 (already a multiple of 3)
41: exponent 2 (needs one more factor to become a multiple of 3)
To make the exponent of 41 equal to 3, we need to multiply by 41(3-2) = 411 = 41.
The smallest number to multiply 5673375 by to yield a perfect cube is 41.
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