72072 has 96 divisors (see below), whose sum is σ = 262080. Its totient is φ = 17280.

The previous prime is 72053. The next prime is 72073. The reversal of 72072 is 27027.

It is a hoax number, since the sum of its digits (18) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is not an unprimeable number, because it can be changed into a prime (72073) by changing a digit.

72072 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 5538 + ... + 5550.

It is an arithmetic number, because the mean of its divisors is an integer number (2730).

2⁷²⁰⁷² is an apocalyptic number.

72072 is a gapful number since it is divisible by the number (72) 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 72072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131040).

72072 is an abundant number, since it is smaller than the sum of its proper divisors (190008).

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

72072 is a wasteful number, since it uses less digits than its factorization.

72072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 43 (or 36 counting only the distinct ones).

The product of its (nonzero) digits is 196, while the sum is 18.

The square root of 72072 is about 268.4622878544. The cubic root of 72072 is about 41.6155390667.

72072 divided by its sum of digits (18) gives a palindrome (4004).

Adding to 72072 its reverse (27027), we get a palindrome (99099).

The spelling of 72072 in words is "seventy-two thousand, seventy-two", and thus it is an iban number.