4101580800 has 720 divisors, whose sum is σ = 16220524320. Its totient is φ = 1021870080.

The previous prime is 4101580793. The next prime is 4101580807. The reversal of 4101580800 is 80851014.

4101580800 is a `hidden beast` number, since 4 + 1 + 0 + 1 + 580 + 80 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (4101580793) and next prime (4101580807).

It is a tau number, because it is divible by the number of its divisors (720).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (4101580807) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 95385579 + ... + 95385621.

It is an arithmetic number, because the mean of its divisors is an integer number (22528506).

Almost surely, 2^4101580800 is an apocalyptic number.

4101580800 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 4101580800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8110262160).

4101580800 is an abundant number, since it is smaller than the sum of its proper divisors (12118943520).

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

4101580800 is a wasteful number, since it uses less digits than its factorization.

4101580800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 110 (or 76 counting only the distinct ones).

The product of its (nonzero) digits is 1280, while the sum is 27.

The square root of 4101580800 is about 64043.5851588588. The cubic root of 4101580800 is about 1600.7263368885.

The spelling of 4101580800 in words is "four billion, one hundred one million, five hundred eighty thousand, eight hundred".