77712 has 20 divisors (see below), whose sum is σ = 200880. Its totient is φ = 25888.

The previous prime is 77711. The next prime is 77713. The reversal of 77712 is 21777.

It is an interprime number because it is at equal distance from previous prime (77711) and next prime (77713).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is not an unprimeable number, because it can be changed into a prime (77711) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 762 + ... + 857.

It is an arithmetic number, because the mean of its divisors is an integer number (10044).

2⁷⁷⁷¹² is an apocalyptic number.

It is an amenable number.

77712 is an abundant number, since it is smaller than the sum of its proper divisors (123168).

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 (100440).

77712 is a wasteful number, since it uses less digits than its factorization.

77712 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1630 (or 1624 counting only the distinct ones).

The product of its digits is 686, while the sum is 24.

The square root of 77712 is about 278.7687213444. The cubic root of 77712 is about 42.6739353936.

The spelling of 77712 in words is "seventy-seven thousand, seven hundred twelve", and thus it is an iban number.