77572 has 24 divisors (see below), whose sum is σ = 155232. Its totient is φ = 33600.

The previous prime is 77569. The next prime is 77573. The reversal of 77572 is 27577.

It is a happy number.

77572 is an admirable number.

It is a nialpdrome in base 11.

It is a self number, because there is not a number n which added to its sum of digits gives 77572.

It is not an unprimeable number, because it can be changed into a prime (77573) by changing a digit.

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 7 ways as a sum of consecutive naturals, for example, 1783 + ... + 1825.

It is an arithmetic number, because the mean of its divisors is an integer number (6468).

2⁷⁷⁵⁷² is an apocalyptic number.

It is an amenable number.

77572 is a primitive abundant number, since it is smaller than the sum of its proper divisors, none of which is abundant.

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (77616).

77572 is a wasteful number, since it uses less digits than its factorization.

77572 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 99 (or 97 counting only the distinct ones).

The product of its digits is 3430, while the sum is 28.

The square root of 77572 is about 278.5175039383. The cubic root of 77572 is about 42.6482939560.

It can be divided in two parts, 77 and 572, that multiplied together give a palindrome (44044).

The spelling of 77572 in words is "seventy-seven thousand, five hundred seventy-two".