# Calculate the Greatest Common Factor or GCF of 280, 21, 58, 7, 3 and 18

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The instructions to find the GCF of 280, 21, 58, 7, 3 and 18 are the next:

## 1. Decompose all numbers into prime factors

280 | 2 |

140 | 2 |

70 | 2 |

35 | 5 |

7 | 7 |

1 |

21 | 3 |

7 | 7 |

1 |

58 | 2 |

29 | 29 |

1 |

7 | 7 |

1 |

3 | 3 |

1 |

18 | 2 |

9 | 3 |

3 | 3 |

1 |

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

Prime factors of 280 | = | 2^{3} . 5 . 7 |

Prime factors of 21 | = | 3 . 7 |

Prime factors of 58 | = | 2 . 29 |

Prime factors of 7 | = | 7 |

Prime factors of 3 | = | 3 |

Prime factors of 18 | = | 2 . 3^{2} |

## 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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