77736 has 32 divisors (see below), whose sum is σ = 201600. Its totient is φ = 24960.

The previous prime is 77731. The next prime is 77743. The reversal of 77736 is 63777.

It is a happy number.

It is a Smith number, since the sum of its digits (30) coincides with the sum of the digits of its prime factors.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 77736.

It is not an unprimeable number, because it can be changed into a prime (77731) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 945 + ... + 1023.

It is an arithmetic number, because the mean of its divisors is an integer number (6300).

2⁷⁷⁷³⁶ 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 77736, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (100800).

77736 is an abundant number, since it is smaller than the sum of its proper divisors (123864).

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

77736 is a wasteful number, since it uses less digits than its factorization.

77736 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 129 (or 125 counting only the distinct ones).

The product of its digits is 6174, while the sum is 30.

The square root of 77736 is about 278.8117644577. The cubic root of 77736 is about 42.6783279757.

It can be divided in two parts, 777 and 36, that multiplied together give a palindrome (27972).

The spelling of 77736 in words is "seventy-seven thousand, seven hundred thirty-six".