77872 has 20 divisors (see below), whose sum is σ = 156736. Its totient is φ = 37440.

The previous prime is 77867. The next prime is 77893. The reversal of 77872 is 27877.

77872 is an admirable number.

It is a Harshad number since it is a multiple of its sum of digits (31).

Its product of digits (5488) is a multiple of the sum of its prime factors (196).

It is a congruent number.

It is an unprimeable number.

77872 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 (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 418 + ... + 574.

2⁷⁷⁸⁷² 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 77872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (78368).

77872 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.

77872 is a wasteful number, since it uses less digits than its factorization.

77872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 196 (or 190 counting only the distinct ones).

The product of its digits is 5488, while the sum is 31.

The square root of 77872 is about 279.0555500254. The cubic root of 77872 is about 42.7032022126.

Subtracting from 77872 its sum of digits (31), we obtain a square (77841 = 279²).

It can be divided in two parts, 77 and 872, that added together give a palindrome (949).

The spelling of 77872 in words is "seventy-seven thousand, eight hundred seventy-two".