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Find the smallest number by which 8768 must be divided so that the quotient is a perfect cube.

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#### Solution

The prime factor of 8768 are

2 | 8768 |

2 | 4384 |

2 | 2192 |

2 | 1096 |

2 | 548 |

2 | 274 |

137 | 137 |

1 |

= 2 x 2 x 2 x 2 x 2 x 2 x 137

= (2 x 2 x 2) x (2 x 2 x 2) x 137

Clearly, 8768 must be divided by 137.

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