38880 has 72 divisors (see below), whose sum is σ = 137592. Its totient is φ = 10368.

The previous prime is 38873. The next prime is 38891. The reversal of 38880 is 8883.

38880 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

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

It is an ABA number since it can be written as A⋅B^{A}, here for A=5, B=6.

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

It is a nialpdrome in base 6.

It is a congruent number.

It is an unprimeable number.

38880 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, 7774 + ... + 7778.

It is an arithmetic number, because the mean of its divisors is an integer number (1911).

2^{38880} is an apocalyptic number.

38880 is a gapful number since it is divisible by the number (30) 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 38880, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (68796).

38880 is an abundant number, since it is smaller than the sum of its proper divisors (98712).

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

38880 is an equidigital number, since it uses as much as digits as its factorization.

38880 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 30 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 27.

The square root of 38880 is about 197.1801207019. The cubic root of 38880 is about 33.8772970397.

The spelling of 38880 in words is "thirty-eight thousand, eight hundred eighty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 32 36 40 45 48 54 60 72 80 81 90 96 108 120 135 144 160 162 180 216 240 243 270 288 324 360 405 432 480 486 540 648 720 810 864 972 1080 1215 1296 1440 1620 1944 2160 2430 2592 3240 3888 4320 4860 6480 7776 9720 12960 19440 38880

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