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

bin | 100111011000000 |

3 | 1000122200 |

4 | 10323000 |

5 | 1121120 |

6 | 233200 |

7 | 112530 |

oct | 47300 |

9 | 30580 |

10 | 20160 |

11 | 14168 |

12 | b800 |

13 | 923a |

14 | 74c0 |

15 | 5e90 |

hex | 4ec0 |

20160 has 84 divisors (see below), whose sum is σ = 79248. Its totient is φ = 4608.

The previous prime is 20149. The next prime is 20161. The reversal of 20160 is 6102.

It is a Jordan-Polya number, since it can be written as 7! ⋅ (2!)^{2}.

It is a tau number, because it is divible by the number of its divisors (84).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 12.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 20160.

It is not an unprimeable number, because it can be changed into a prime (20161) by changing a digit.

20160 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2877 + ... + 2883.

20160 is a highly composite number, because it has more divisors than any smaller number.

2^{20160} is an apocalyptic number.

20160 is a gapful number since it is divisible by the number (20) 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 20160, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (39624).

20160 is an abundant number, since it is smaller than the sum of its proper divisors (59088).

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

20160 is a wasteful number, since it uses less digits than its factorization.

20160 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 30 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 12, while the sum is 9.

The square root of 20160 is about 141.9859147944. The cubic root of 20160 is about 27.2163684638.

Adding to 20160 its reverse (6102), we get a palindrome (26262).

The spelling of 20160 in words is "twenty thousand, one hundred sixty".

Divisors: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 28 30 32 35 36 40 42 45 48 56 60 63 64 70 72 80 84 90 96 105 112 120 126 140 144 160 168 180 192 210 224 240 252 280 288 315 320 336 360 420 448 480 504 560 576 630 672 720 840 960 1008 1120 1260 1344 1440 1680 2016 2240 2520 2880 3360 4032 5040 6720 10080 20160

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