4635640800 has 1152 divisors, whose sum is σ = 21118648320. Its totient is φ = 958003200.

The previous prime is 4635640787. The next prime is 4635640811. The reversal of 4635640800 is 80465364.

4635640800 is a `hidden beast` number, since 4 + 6 + 3 + 5 + 640 + 8 + 0 + 0 = 666.

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 107805579 + ... + 107805621.

It is an arithmetic number, because the mean of its divisors is an integer number (18332160).

Almost surely, 2^4635640800 is an apocalyptic number.

4635640800 is a gapful number since it is divisible by the number (40) 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 4635640800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10559324160).

4635640800 is an abundant number, since it is smaller than the sum of its proper divisors (16483007520).

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

4635640800 is a wasteful number, since it uses less digits than its factorization.

4635640800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 133 (or 114 counting only the distinct ones).

The product of its (nonzero) digits is 69120, while the sum is 36.

The square root of 4635640800 is about 68085.5403151066. The cubic root of 4635640800 is about 1667.3876951369.

The spelling of 4635640800 in words is "four billion, six hundred thirty-five million, six hundred forty thousand, eight hundred".