What is the prime factorization of 4998?

We draw a vertical line and write 4998 to the left of the line:

4998 |

4998 is divisible by 17

4998 : 17 = 294

We write 17 (the divisor) to the right of the line and 294 to the left of the line:

4998 | 17 |

294 |

17 is a prime number.

294 is not a prime number.

See Prime numbers 1 through 300.

294 is divisible by 6

294 : 6 =

294 : (2 * 3) = 49

294 : (2 * 3) = 49

We write (2 * 3) (the divisor) to the right of the line and 49 to the left of the line:

4998 | 17 |

294 | 2 * 3 |

49 |

49 is divisible by 7

49 : 7 = 7

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

4998 | 17 |

294 | 2 * 3 |

49 | 7 |

7 |

7 is a prime number. 7 is divisible by itself and by 1. We divide 7 by 7:

7 : 7 = 1

and write 7 (the divisor) to the right of the line and 1 to the left of the line:

4998 | 17 |

294 | 2 * 3 |

49 | 7 |

7 | 7 |

1 |

The numbers to the right of the line are prime factors of the number 4998.

Therefore, the prime factorization of 4998 is

4998 =

2 * 3 * 7 * 7 * 17

2 * 3 * 7 * 7 * 17

The prime factorization of 4998 using exponents

4998 =

2 * 3 * 7^{2} * 17

2 * 3 * 7

So, the prime factors of 4998 are

2, 3, 7, 7, 17