# Calculate the Greatest Common Factor or GCF of 15 and 108

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The instructions to find the GCF of 15 and 108 are the next:

## 1. Decompose all numbers into prime factors

15 | 3 |

5 | 5 |

1 |

108 | 2 |

54 | 2 |

27 | 3 |

9 | 3 |

3 | 3 |

1 |

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

Prime factors of 15 | = | 3 . 5 |

Prime factors of 108 | = | 2^{2} . 3^{3} |

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

Common prime factors: 3

Common prime factors with the lowest exponent: 3^{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** = 3^{1} = 3

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