72031680 has 280 divisors, whose sum is σ = 293571168. Its totient is φ = 16422912.

The previous prime is 72031657. The next prime is 72031691. The reversal of 72031680 is 8613027.

It is a tau number, because it is divible by the number of its divisors (280).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 181242 + ... + 181638.

Almost surely, 2^72031680 is an apocalyptic number.

72031680 is a gapful number since it is divisible by the number (70) 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 72031680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (146785584).

72031680 is an abundant number, since it is smaller than the sum of its proper divisors (221539488).

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

72031680 is a wasteful number, since it uses less digits than its factorization.

72031680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 433 (or 414 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 72031680 is about 8487.1479308423. The cubic root of 72031680 is about 416.0777714557.

It can be divided in two parts, 720 and 31680, that added together give a square (32400 = 180²).

The spelling of 72031680 in words is "seventy-two million, thirty-one thousand, six hundred eighty".