4116096000 has 440 divisors, whose sum is σ = 15378390456. Its totient is φ = 1094860800.

The previous prime is 4116095983. The next prime is 4116096007. The reversal of 4116096000 is 6906114.

4116096000 is a `hidden beast` number, since 41 + 16 + 0 + 9 + 600 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 65028096 + 4051067904 = 8064^2 + 63648^2 .

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 (4116096007) by changing a digit.

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 39 ways as a sum of consecutive naturals, for example, 10367802 + ... + 10368198.

Almost surely, 2^4116096000 is an apocalyptic number.

4116096000 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 4116096000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7689195228).

4116096000 is an abundant number, since it is smaller than the sum of its proper divisors (11262294456).

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

4116096000 is an equidigital number, since it uses as much as digits as its factorization.

4116096000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 444 (or 407 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

The square root of 4116096000 is about 64156.8079006429. The cubic root of 4116096000 is about 1602.6123989525.

The spelling of 4116096000 in words is "four billion, one hundred sixteen million, ninety-six thousand".