31104 has 48 divisors (see below), whose sum is σ = 92820. Its totient is φ = 10368.

The previous prime is 31091. The next prime is 31121. The reversal of 31104 is 40113.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as 4! ⋅ (3!)^{4}.

31104 is nontrivially palindromic in base 15.

It is a tau number, because it is divible by the number of its divisors (48).

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

It is a nialpdrome in base 6.

It is a zygodrome in base 2.

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 31104.

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 10367 + 10368 + 10369.

2^{31104} 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 31104, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (46410).

31104 is an abundant number, since it is smaller than the sum of its proper divisors (61716).

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

31104 is an frugal number, since it uses more digits than its factorization.

31104 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 29 (or 5 counting only the distinct ones).

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

The square root of 31104 is about 176.3632614804. The cubic root of 31104 is about 31.4488967305.

Multiplying 31104 by its product of nonzero digits (12), we get a cube (373248 = 72^{3}).

Adding to 31104 its reverse (40113), we get a palindrome (71217).

Subtracting 31104 from its reverse (40113), we obtain a palindrome (9009).

The spelling of 31104 in words is "thirty-one thousand, one hundred four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192 216 243 288 324 384 432 486 576 648 864 972 1152 1296 1728 1944 2592 3456 3888 5184 7776 10368 15552 31104

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