# prime factorizations of some small highly composite numbers

All highly composite numbers have prime factorizations^{} containing consecutive prime numbers^{}, starting with 2, while the exponents form a sequence in descending order^{} (the number 1 as an exponent is tacit in the following table).

HCN | Factorization |
---|---|

4 | ${2}^{2}$ |

6 | $2\times 3$ |

12 | ${2}^{2}\times 3$ |

24 | ${2}^{3}\times 3$ |

36 | ${2}^{2}\times {3}^{2}$ |

48 | ${2}^{4}\times 3$ |

60 | ${2}^{2}\times 3\times 5$ |

120 | ${2}^{3}\times 3\times 5$ |

180 | ${2}^{2}\times {3}^{2}\times 5$ |

240 | ${2}^{4}\times 3\times 5$ |

360 | ${2}^{3}\times {3}^{2}\times 5$ |

720 | ${2}^{4}\times {3}^{2}\times 5$ |

840 | ${2}^{3}\times 3\times 5\times 7$ |

1260 | ${2}^{2}\times {3}^{2}\times 5\times 7$ |

1680 | ${2}^{4}\times 3\times 5\times 7$ |

2520 | ${2}^{3}\times {3}^{2}\times 5\times 7$ |

5040 | ${2}^{4}\times {3}^{2}\times 5\times 7$ |

7560 | ${2}^{3}\times {3}^{3}\times 5\times 7$ |

10080 | ${2}^{5}\times {3}^{2}\times 5\times 7$ |

15120 | ${2}^{4}\times {3}^{3}\times 5\times 7$ |

20160 | ${2}^{6}\times {3}^{2}\times 5\times 7$ |

25200 | ${2}^{4}\times {3}^{2}\times {5}^{2}\times 7$ |

27720 | ${2}^{3}\times {3}^{2}\times 5\times 7\times 11$ |

45360 | ${2}^{4}\times {3}^{4}\times 5\times 7$ |

50400 | ${2}^{5}\times {3}^{2}\times {5}^{2}\times 7$ |

55440 | ${2}^{4}\times {3}^{2}\times 5\times 7\times 11$ |

83160 | ${2}^{3}\times {3}^{3}\times 5\times 7\times 11$ |

110880 | ${2}^{5}\times {3}^{2}\times 5\times 7\times 11$ |

166320 | ${2}^{4}\times {3}^{3}\times 5\times 7\times 11$ |

221760 | ${2}^{6}\times {3}^{2}\times 5\times 7\times 11$ |

277200 | ${2}^{4}\times {3}^{2}\times {5}^{2}\times 7\times 11$ |

332640 | ${2}^{5}\times {3}^{3}\times 5\times 7\times 11$ |

498960 | ${2}^{4}\times {3}^{4}\times 5\times 7\times 11$ |

554400 | ${2}^{5}\times {3}^{2}\times {5}^{2}\times 7\times 11$ |

665280 | ${2}^{6}\times {3}^{3}\times 5\times 7\times 11$ |

720720 | ${2}^{4}\times {3}^{2}\times 5\times 7\times 11\times 13$ |

1081080 | ${2}^{3}\times {3}^{3}\times 5\times 7\times 11\times 13$ |

1441440 | ${2}^{5}\times {3}^{2}\times 5\times 7\times 11\times 13$ |

2162160 | ${2}^{4}\times {3}^{3}\times 5\times 7\times 11\times 13$ |

Title | prime factorizations of some small highly composite numbers |
---|---|

Canonical name | PrimeFactorizationsOfSomeSmallHighlyCompositeNumbers |

Date of creation | 2013-03-22 18:51:29 |

Last modified on | 2013-03-22 18:51:29 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 5 |

Author | PrimeFan (13766) |

Entry type | Example |

Classification | msc 11N56 |