# Calculate the Greatest Common Factor or GCF of 180, 340, 450 and 500

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The instructions to find the GCF of 180, 340, 450 and 500 are the next:

## 1. Decompose all numbers into prime factors

180 | 2 |

90 | 2 |

45 | 3 |

15 | 3 |

5 | 5 |

1 |

340 | 2 |

170 | 2 |

85 | 5 |

17 | 17 |

1 |

450 | 2 |

225 | 3 |

75 | 3 |

25 | 5 |

5 | 5 |

1 |

500 | 2 |

250 | 2 |

125 | 5 |

25 | 5 |

5 | 5 |

1 |

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

Prime factors of 180 | = | 2^{2} . 3^{2} . 5 |

Prime factors of 340 | = | 2^{2} . 5 . 17 |

Prime factors of 450 | = | 2 . 3^{2} . 5^{2} |

Prime factors of 500 | = | 2^{2} . 5^{3} |

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

Common prime factors: 2 , 5

Common prime factors with the lowest exponent: 2^{1}, 5^{1}

## 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.

**GCF** = 2^{1}. 5^{1} = 10

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