# By what smallest natural number should -17496 be divided so that the quotient become a prefect cube

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Answer

3 should be divided to -17496 to get prefect cube

prime factors of -17496= -2×2×2×3×3×3×3×3×3×3

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**Answer:**

*3 *

**Step-by-step explanation:**

__ 17496__ = 2×8748 = 2×2×4374 = 2×2×2×2187 = 2×2×2×3×729 = 2×2×2×3×3×243 = 2×2×2×3×3×3×81 = 2×2×2×3×3×3×3×27 = 2×2×2×3×3×3×3×3×9 =

__= 2³× =__

*2×2×2×3×3×3×3×3×3×3*

*(2³×9³)×3*- 17496 ÷ ** 3** = - 5832 = ( - 18)³

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