77564400 has 120 divisors (see below), whose sum is σ = 251166960. Its totient is φ = 20459520.

The previous prime is 77564381. The next prime is 77564411. The reversal of 77564400 is 446577.

It is a tau number, because it is divible by the number of its divisors (120).

It is a super-2 number, since 2×77564400² = 12032472294720000, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 130504 + ... + 131096.

It is an arithmetic number, because the mean of its divisors is an integer number (2093058).

Almost surely, 2^77564400 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 77564400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (125583480).

77564400 is an abundant number, since it is smaller than the sum of its proper divisors (173602560).

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

77564400 is a wasteful number, since it uses less digits than its factorization.

77564400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 723 (or 712 counting only the distinct ones).

The product of its (nonzero) digits is 23520, while the sum is 33.

The square root of 77564400 is about 8807.0653455053. The cubic root of 77564400 is about 426.4690110967.

The spelling of 77564400 in words is "seventy-seven million, five hundred sixty-four thousand, four hundred".