72576 has 80 divisors (see below), whose sum is σ = 246840. Its totient is φ = 20736.

The previous prime is 72559. The next prime is 72577. The reversal of 72576 is 67527.

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

Its product of digits (2940) is a multiple of the sum of its prime divisors (12).

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 72576.

It is not an unprimeable number, because it can be changed into a prime (72577) by changing a digit.

72576 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 9 ways as a sum of consecutive naturals, for example, 10365 + ... + 10371.

72576 is a Friedman number, since it can be written as 567*2^7, using all its digits and the basic arithmetic operations.

2^{72576} 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 72576, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (123420).

72576 is an abundant number, since it is smaller than the sum of its proper divisors (174264).

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

72576 is an equidigital number, since it uses as much as digits as its factorization.

72576 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 33 (or 12 counting only the distinct ones).

The product of its digits is 2940, while the sum is 27.

The square root of 72576 is about 269.3993318477. The cubic root of 72576 is about 41.7123197386.

The spelling of 72576 in words is "seventy-two thousand, five hundred seventy-six".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 32 36 42 48 54 56 63 64 72 81 84 96 108 112 126 128 144 162 168 189 192 216 224 252 288 324 336 378 384 432 448 504 567 576 648 672 756 864 896 1008 1134 1152 1296 1344 1512 1728 2016 2268 2592 2688 3024 3456 4032 4536 5184 6048 8064 9072 10368 12096 18144 24192 36288 72576

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