4101688800 has 576 divisors, whose sum is σ = 16506443520. Its totient is φ = 974592000.

The previous prime is 4101688777. The next prime is 4101688807. The reversal of 4101688800 is 88861014.

4101688800 is a `hidden beast` number, since 410 + 168 + 8 + 80 + 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 not an unprimeable number, because it can be changed into a prime (4101688807) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 14493459 + ... + 14493741.

It is an arithmetic number, because the mean of its divisors is an integer number (28657020).

Almost surely, 2^4101688800 is an apocalyptic number.

4101688800 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 4101688800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8253221760).

4101688800 is an abundant number, since it is smaller than the sum of its proper divisors (12404754720).

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

4101688800 is a wasteful number, since it uses less digits than its factorization.

4101688800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 384 (or 365 counting only the distinct ones).

The product of its (nonzero) digits is 12288, while the sum is 36.

The square root of 4101688800 is about 64044.4283290904. The cubic root of 4101688800 is about 1600.7403865062.

The spelling of 4101688800 in words is "four billion, one hundred one million, six hundred eighty-eight thousand, eight hundred".