103584096 has 288 divisors, whose sum is σ = 383056128. Its totient is φ = 26749440.

The previous prime is 103584031. The next prime is 103584097. The reversal of 103584096 is 690485301.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-3 number, since 3×103584096³ (a number of 25 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a nialpdrome in base 14.

It is a self number, because there is not a number n which added to its sum of digits gives 103584096.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (103584097) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 598666 + ... + 598838.

It is an arithmetic number, because the mean of its divisors is an integer number (1330056).

Almost surely, 2^103584096 is an apocalyptic number.

103584096 is a gapful number since it is divisible by the number (16) 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 103584096, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (191528064).

103584096 is an abundant number, since it is smaller than the sum of its proper divisors (279472032).

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

103584096 is a wasteful number, since it uses less digits than its factorization.

103584096 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 216 (or 196 counting only the distinct ones).

The product of its (nonzero) digits is 25920, while the sum is 36.

The square root of 103584096 is about 10177.6272283868. The cubic root of 103584096 is about 469.6392221525.

The spelling of 103584096 in words is "one hundred three million, five hundred eighty-four thousand, ninety-six".