77112 has 80 divisors (see below), whose sum is σ = 261360. Its totient is φ = 20736.

The previous prime is 77101. The next prime is 77137. The reversal of 77112 is 21177.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nude number because it is divisible by every one of its digits.

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 77112.

It is an unprimeable number.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 4528 + ... + 4544.

It is an arithmetic number, because the mean of its divisors is an integer number (3267).

2⁷⁷¹¹² is an apocalyptic number.

77112 is a gapful number since it is divisible by the number (72) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77112, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (130680).

77112 is an abundant number, since it is smaller than the sum of its proper divisors (184248).

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

77112 is a wasteful number, since it uses less digits than its factorization.

77112 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 42 (or 29 counting only the distinct ones).

The product of its digits is 98, while the sum is 18.

The square root of 77112 is about 277.6904751697. The cubic root of 77112 is about 42.5638256685.

Adding to 77112 its reverse (21177), we get a palindrome (98289).

The spelling of 77112 in words is "seventy-seven thousand, one hundred twelve", and thus it is an iban number.