65880 has 64 divisors (see below), whose sum is σ = 223200. Its totient is φ = 17280.

The previous prime is 65867. The next prime is 65881. The reversal of 65880 is 8856.

65880 is a *`hidden beast`* number, since 658 + 8 + 0 = 666.

It is a Smith number, since the sum of its digits (27) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 65880.

It is not an unprimeable number, because it can be changed into a prime (65881) by changing a digit.

65880 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1050 + ... + 1110.

2^{65880} is an apocalyptic number.

65880 is a gapful number since it is divisible by the number (60) 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 65880, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (111600).

65880 is an abundant number, since it is smaller than the sum of its proper divisors (157320).

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

65880 is a wasteful number, since it uses less digits than its factorization.

65880 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 81 (or 71 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 27.

The square root of 65880 is about 256.6709956345. The cubic root of 65880 is about 40.3878929836.

It can be divided in two parts, 6 and 5880, that added together give a triangular number (5886 = T_{108}).

The spelling of 65880 in words is "sixty-five thousand, eight hundred eighty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 18 20 24 27 30 36 40 45 54 60 61 72 90 108 120 122 135 180 183 216 244 270 305 360 366 488 540 549 610 732 915 1080 1098 1220 1464 1647 1830 2196 2440 2745 3294 3660 4392 5490 6588 7320 8235 10980 13176 16470 21960 32940 65880

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