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45864 = 23327213
BaseRepresentation
bin1011001100101000
32022220200
423030220
52431424
6552200
7250500
oct131450
968820
1045864
1131505
1222660
1317b50
1412a00
15d8c9
hexb328

45864 has 72 divisors (see below), whose sum is σ = 155610. Its totient is φ = 12096.

The previous prime is 45863. The next prime is 45869. The reversal of 45864 is 46854.

Subtracting from 45864 its product of digits (3840), we obtain a palindrome (42024).

Subtracting 45864 from its reverse (46854), we obtain a triangular number (990 = T44).

It can be divided in two parts, 45 and 864, that added together give a palindrome (909).

It can be written as a sum of positive squares in only one way, i.e., 44100 + 1764 = 210^2 + 42^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is a nialpdrome in base 6.

It is a zygodrome in base 6.

It is not an unprimeable number, because it can be changed into a prime (45863) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 3522 + ... + 3534.

45864 is a Friedman number, since it can be written as 546*84, using all its digits and the basic arithmetic operations.

245864 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 45864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (77805).

45864 is an abundant number, since it is smaller than the sum of its proper divisors (109746).

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

45864 is a wasteful number, since it uses less digits than its factorization.

45864 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 39 (or 25 counting only the distinct ones).

The product of its digits is 3840, while the sum is 27.

The square root of 45864 is about 214.1588195709. The cubic root of 45864 is about 35.7951326570.

The spelling of 45864 in words is "forty-five thousand, eight hundred sixty-four".

Divisors: 1 2 3 4 6 7 8 9 12 13 14 18 21 24 26 28 36 39 42 49 52 56 63 72 78 84 91 98 104 117 126 147 156 168 182 196 234 252 273 294 312 364 392 441 468 504 546 588 637 728 819 882 936 1092 1176 1274 1638 1764 1911 2184 2548 3276 3528 3822 5096 5733 6552 7644 11466 15288 22932 45864