83764800 has 336 divisors, whose sum is σ = 350235520. Its totient is φ = 19077120.

The previous prime is 83764783. The next prime is 83764801. The reversal of 83764800 is 846738.

83764800 is a `hidden beast` number, since 8 + 3 + 7 + 648 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (336).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (83764801) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 302262 + ... + 302538.

Almost surely, 2^83764800 is an apocalyptic number.

83764800 is a gapful number since it is divisible by the number (80) 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 83764800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (175117760).

83764800 is an abundant number, since it is smaller than the sum of its proper divisors (266470720).

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

83764800 is a wasteful number, since it uses less digits than its factorization.

83764800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 315 (or 294 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The square root of 83764800 is about 9152.3111835208. The cubic root of 83764800 is about 437.5427767697.

The spelling of 83764800 in words is "eighty-three million, seven hundred sixty-four thousand, eight hundred".