• 77 can be written using four 4's:

• Deleting all the even digits from 2^{77} = 151115727451828646838272 we obtain a prime (151115775137).

77 has 4 divisors (see below), whose sum is σ = 96. Its totient is φ = 60.

The previous prime is 73. The next prime is 79.

77 is nontrivially palindromic in base 10.

77 is an esthetic number in base 12, because in such base its adjacent digits differ by 1.

It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4.

It is a cyclic number.

It is not a de Polignac number, because 77 - 2^{2} = 73 is a prime.

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

It is an Ulam number.

It is a Duffinian number.

It is a partition number, being equal to the number of ways a set of 12 identical objects can be partitioned into subset.

77 is a nontrivial repdigit in base 10.

It is a plaindrome in base 8, base 10, base 13, base 14 and base 16.

It is a nialpdrome in base 9, base 10, base 11, base 12 and base 15.

It is a zygodrome in base 10.

It is a congruent number.

It is a panconsummate number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2 + ... + 12.

It is an arithmetic number, because the mean of its divisors is an integer number (24).

It is an amenable number.

77 is a deficient number, since it is larger than the sum of its proper divisors (19).

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

With its successor (78) it forms a Ruth-Aaron pair, since the sum of their distinct prime factors is the same (18).

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

The sum of its prime factors is 18.

The product of its digits is 49, while the sum is 14.

The square root of 77 is about 8.7749643874. The cubic root of 77 is about 4.2543208651.

Adding to 77 its sum of digits (14), we get a triangular number (91 = T_{13}).

Subtracting from 77 its product of digits (49), we obtain a triangular number (28 = T_{7}).

Multiplying 77 by its product of digits (49), we get a palindrome (3773).

The spelling of 77 in words is "seventy-seven", and thus it is an aban number, an iban number, an oban number, and an uban number.

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