72306 has 32 divisors (see below), whose sum is σ = 174720. Its totient is φ = 22032.

The previous prime is 72287. The next prime is 72307. The reversal of 72306 is 60327.

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 (72307) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 651 + ... + 753.

It is an arithmetic number, because the mean of its divisors is an integer number (5460).

2⁷²³⁰⁶ is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72306, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (87360).

72306 is an abundant number, since it is smaller than the sum of its proper divisors (102414).

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

72306 is a wasteful number, since it uses less digits than its factorization.

72306 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 127 (or 121 counting only the distinct ones).

The product of its (nonzero) digits is 252, while the sum is 18.

The square root of 72306 is about 268.8977500836. The cubic root of 72306 is about 41.6605288737.

It can be divided in two parts, 72 and 306, that added together give a triangular number (378 = T₂₇).

The spelling of 72306 in words is "seventy-two thousand, three hundred six".