72105984 has 120 divisors (see below), whose sum is σ = 214951520. Its totient is φ = 23887872.

The previous prime is 72105983. The next prime is 72105991. The reversal of 72105984 is 48950127.

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

It is not an unprimeable number, because it can be changed into a prime (72105983) by changing a digit.

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 7 ways as a sum of consecutive naturals, for example, 442287 + ... + 442449.

Almost surely, 2^72105984 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 72105984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (107475760).

72105984 is an abundant number, since it is smaller than the sum of its proper divisors (142845536).

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

72105984 is an equidigital number, since it uses as much as digits as its factorization.

72105984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 200 (or 168 counting only the distinct ones).

The product of its (nonzero) digits is 20160, while the sum is 36.

The square root of 72105984 is about 8491.5242447985. The cubic root of 72105984 is about 416.2207900938.

The spelling of 72105984 in words is "seventy-two million, one hundred five thousand, nine hundred eighty-four".