72360 has 64 divisors (see below), whose sum is σ = 244800. Its totient is φ = 19008.

The previous prime is 72353. The next prime is 72367. The reversal of 72360 is 6327.

It is a Cunningham number, because it is equal to 269²-1.

It is an interprime number because it is at equal distance from previous prime (72353) and next prime (72367).

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 (72367) by changing a digit.

72360 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1047 + ... + 1113.

It is an arithmetic number, because the mean of its divisors is an integer number (3825).

2⁷²³⁶⁰ 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 72360, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (122400).

72360 is an abundant number, since it is smaller than the sum of its proper divisors (172440).

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

72360 is a wasteful number, since it uses less digits than its factorization.

72360 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 77 counting only the distinct ones).

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

The square root of 72360 is about 268.9981412575. The cubic root of 72360 is about 41.6708973482.

Adding to 72360 its reverse (6327), we get a palindrome (78687).

The spelling of 72360 in words is "seventy-two thousand, three hundred sixty".