77520 has 80 divisors (see below), whose sum is σ = 267840. Its totient is φ = 18432.

The previous prime is 77513. The next prime is 77521. The reversal of 77520 is 2577.

77520 is a nontrivial binomial coefficient, being equal to C(20, 7).

It is a tau number, because it is divible by the number of its divisors (80).

It is a super-4 number, since 4×77520⁴ (a number of 21 digits) contains 4444 as substring.

It is a nialpdrome in base 10.

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 77520.

It is not an unprimeable number, because it can be changed into a prime (77521) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 4071 + ... + 4089.

It is an arithmetic number, because the mean of its divisors is an integer number (3348).

2⁷⁷⁵²⁰ 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 77520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (133920).

77520 is an abundant number, since it is smaller than the sum of its proper divisors (190320).

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

77520 is a wasteful number, since it uses less digits than its factorization.

77520 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 52 (or 46 counting only the distinct ones).

The product of its (nonzero) digits is 490, while the sum is 21.

The square root of 77520 is about 278.4241368847. The cubic root of 77520 is about 42.6387621360.

The spelling of 77520 in words is "seventy-seven thousand, five hundred twenty".