# Calculate the Greatest Common Factor or GCF of 112, 84 and 27

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The instructions to find the GCF of 112, 84 and 27 are the next:

## 1. Decompose all numbers into prime factors

112 | 2 |

56 | 2 |

28 | 2 |

14 | 2 |

7 | 7 |

1 |

84 | 2 |

42 | 2 |

21 | 3 |

7 | 7 |

1 |

27 | 3 |

9 | 3 |

3 | 3 |

1 |

## 2. Write all numbers as the product of its prime factors

Prime factors of 112 | = | 2^{4} . 7 |

Prime factors of 84 | = | 2^{2} . 3 . 7 |

Prime factors of 27 | = | 3^{3} |

## 3. Choose the common prime factors with the lowest exponent

Common prime factors: None

Common prime factors with the lowest exponent: None

## 4. Calculate the Greatest Common Factor or GCF

Remember, to find the GCF of several numbers you must multiply the common prime factors with the lowest exponent.

Since there are not common prime factors the **GCF** is 1

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