77724864 has 168 divisors, whose sum is σ = 261993888. Its totient is φ = 21565440.

The previous prime is 77724863. The next prime is 77724869. The reversal of 77724864 is 46842777.

It is a tau number, because it is divible by the number of its divisors (168).

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

It is not an unprimeable number, because it can be changed into a prime (77724863) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 148924 + ... + 149444.

Almost surely, 2^77724864 is an apocalyptic number.

77724864 is a gapful number since it is divisible by the number (74) 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 77724864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (130996944).

77724864 is an abundant number, since it is smaller than the sum of its proper divisors (184269024).

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

77724864 is a wasteful number, since it uses less digits than its factorization.

77724864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 583 (or 570 counting only the distinct ones).

The product of its digits is 526848, while the sum is 45.

The square root of 77724864 is about 8816.1705972605. The cubic root of 77724864 is about 426.7628993005.

The spelling of 77724864 in words is "seventy-seven million, seven hundred twenty-four thousand, eight hundred sixty-four".