77686560 has 288 divisors, whose sum is σ = 317157120. Its totient is φ = 17708544.

The previous prime is 77686541. The next prime is 77686577. The reversal of 77686560 is 6568677.

77686560 is a `hidden beast` number, since 7 + 7 + 6 + 86 + 560 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-3 number, since 3×77686560³ (a number of 25 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 211497 + ... + 211863.

It is an arithmetic number, because the mean of its divisors is an integer number (1101240).

Almost surely, 2^77686560 is an apocalyptic number.

77686560 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77686560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (158578560).

77686560 is an abundant number, since it is smaller than the sum of its proper divisors (239470560).

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

77686560 is a wasteful number, since it uses less digits than its factorization.

77686560 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 405 (or 384 counting only the distinct ones).

The product of its (nonzero) digits is 423360, while the sum is 45.

The square root of 77686560 is about 8813.9979577942. The cubic root of 77686560 is about 426.6927826896.

The spelling of 77686560 in words is "seventy-seven million, six hundred eighty-six thousand, five hundred sixty".