7828128000 has 864 divisors, whose sum is σ = 35217891072. Its totient is φ = 1622016000.

The previous prime is 7828127969. The next prime is 7828128013. The reversal of 7828128000 is 8218287.

It is a super-2 number, since 2×7828128000² (a number of 21 digits) contains 22 as substring.

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

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 95 ways as a sum of consecutive naturals, for example, 22175824 + ... + 22176176.

It is an arithmetic number, because the mean of its divisors is an integer number (40761448).

Almost surely, 2^7828128000 is an apocalyptic number.

7828128000 is a gapful number since it is divisible by the number (70) 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 7828128000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17608945536).

7828128000 is an abundant number, since it is smaller than the sum of its proper divisors (27389763072).

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

7828128000 is a wasteful number, since it uses less digits than its factorization.

7828128000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 408 (or 381 counting only the distinct ones).

The product of its (nonzero) digits is 14336, while the sum is 36.

The square root of 7828128000 is about 88476.7087995479. The cubic root of 7828128000 is about 1985.5735219054.

The spelling of 7828128000 in words is "seven billion, eight hundred twenty-eight million, one hundred twenty-eight thousand".