Question

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

Answer 1

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

Answer 2

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 = 2×2×2×3×3×3×3×3×3×3 = 2³× $3^{7}$ = (2³×9³)×3

- 17496 ÷ 3 = - 5832 = ( - 18)³