Base | Representation |
---|---|

bin | 110100101111000000000 |

3 | 10020210101000 |

4 | 12211320000 |

5 | 420244000 |

6 | 101012000 |

7 | 20454621 |

oct | 6457000 |

9 | 3223330 |

10 | 1728000 |

11 | a802aa |

12 | 6b4000 |

13 | 4866b1 |

14 | 32da48 |

15 | 242000 |

hex | 1a5e00 |

1728000 has 160 divisors (see below), whose sum is σ = 6383520. Its totient is φ = 460800.

The previous prime is 1727989. The next prime is 1728017. The reversal of 1728000 is 8271.

The cubic root of 1728000 is 120.

It is a perfect power (a cube), and thus also a powerful number.

It is a Jordan-Polya number, since it can be written as (5!)^{3}.

It is a tau number, because it is divible by the number of its divisors (160).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 345598 + ... + 345602.

It is an arithmetic number, because the mean of its divisors is an integer number (39897).

2^{1728000} is an apocalyptic number.

1728000 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (3191760).

1728000 is an abundant number, since it is smaller than the sum of its proper divisors (4655520).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

1728000 is an frugal number, since it uses more digits than its factorization.

1728000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 42 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 112, while the sum is 18.

The square root of 1728000 is about 1314.5341380124.

The spelling of 1728000 in words is "one million, seven hundred twenty-eight thousand".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54 60 64 72 75 80 90 96 100 108 120 125 128 135 144 150 160 180 192 200 216 225 240 250 256 270 288 300 320 360 375 384 400 432 450 480 500 512 540 576 600 640 675 720 750 768 800 864 900 960 1000 1080 1125 1152 1200 1280 1350 1440 1500 1536 1600 1728 1800 1920 2000 2160 2250 2304 2400 2560 2700 2880 3000 3200 3375 3456 3600 3840 4000 4320 4500 4608 4800 5400 5760 6000 6400 6750 6912 7200 7680 8000 8640 9000 9600 10800 11520 12000 12800 13500 13824 14400 16000 17280 18000 19200 21600 23040 24000 27000 28800 32000 34560 36000 38400 43200 48000 54000 57600 64000 69120 72000 86400 96000 108000 115200 144000 172800 192000 216000 288000 345600 432000 576000 864000 1728000

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