What is the prime factorization of 19992?

We draw a vertical line and write 19992 to the left of the line:

19992 |

19992 is divisible by 7

19992 : 7 = 2856

We write 7 (the divisor) to the right of the line and 2856 to the left of the line:

19992 | 7 |

2856 |

7 is a prime number.

2856 is not a prime number.

2856 is divisible by 7:

2856 : 7 = 408

We write 7 (the divisor) to the right of the line and 408 to the left of the line:

19992 | 7 |

2856 | 7 |

408 |

408 is divisible by 6:

408 : 6 =

408 : (2 * 3) = 68

408 : (2 * 3) = 68

We write (2 * 3) (the divisor) to the right of the line and 68 to the left of the line:

19992 | 7 |

2856 | 7 |

408 | 2 * 3 |

68 |

68 is divisible by 4:

68 : 4 = 68 : (2 * 2) = 17

We write (2 * 2) (the divisor) to the right of the line and 17 to the left of the line:

19992 | 7 |

2856 | 7 |

408 | 2 * 3 |

68 | 2 * 2 |

17 |

17 is a prime number. 17 is divisible by itself and by 1. We divide 17 by 17:

17 : 17 = 1

and write 17 (the divisor) to the right of the line and 1 to the left of the line:

19992 | 7 |

2856 | 7 |

408 | 2 * 3 |

68 | 2 * 2 |

17 | 17 |

1 |

The numbers to the right of the line are prime factors of the number 19992.

Therefore, the prime factorization of 19992 is

19992 =

2 * 2 * 2 * 3 * 7 * 7 * 17

2 * 2 * 2 * 3 * 7 * 7 * 17

The prime factorization of 19992 using exponents

19992 =

2^{3} * 3 * 7^{2} * 17

2

So, the prime factors of 19992 are

2, 2, 2, 3, 7, 7, 17