72084168 has 160 divisors (see below), whose sum is σ = 223608000. Its totient is φ = 21555072.

The previous prime is 72084167. The next prime is 72084179. The reversal of 72084168 is 86148027.

It is a super-2 number, since 2×72084168² = 10392254552504448, which contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72084163) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 362133 + ... + 362331.

It is an arithmetic number, because the mean of its divisors is an integer number (1397550).

Almost surely, 2^72084168 is an apocalyptic number.

72084168 is a gapful number since it is divisible by the number (78) 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 72084168, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (111804000).

72084168 is an abundant number, since it is smaller than the sum of its proper divisors (151523832).

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

72084168 is a wasteful number, since it uses less digits than its factorization.

72084168 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 273 (or 260 counting only the distinct ones).

The product of its (nonzero) digits is 21504, while the sum is 36.

The square root of 72084168 is about 8490.2395725916. The cubic root of 72084168 is about 416.1788093493.

The spelling of 72084168 in words is "seventy-two million, eighty-four thousand, one hundred sixty-eight".