128178320400 has 1215 divisors, whose sum is σ = 531315009381. Its totient is φ = 29695610880.

The previous prime is 128178320339. The next prime is 128178320441. The reversal of 128178320400 is 4023871821.

The square root of 128178320400 is 358020.

It is a perfect power (a square), and thus also a powerful number.

128178320400 is a `hidden beast` number, since 128 + 178 + 320 + 40 + 0 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 93349803024 + 34828517376 = 305532^2 + 186624^2 .

It is a tau number, because it is divible by the number of its divisors (1215).

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

It is an unprimeable number.

It is a polite number, since it can be written in 242 ways as a sum of consecutive naturals, for example, 7539901192 + ... + 7539901208.

Almost surely, 2^128178320400 is an apocalyptic number.

128178320400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

128178320400 is the 358020-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 128178320400

128178320400 is an abundant number, since it is smaller than the sum of its proper divisors (403136688981).

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

128178320400 is an equidigital number, since it uses as much as digits as its factorization.

128178320400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 102 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 21504, while the sum is 36.

Multiplying 128178320400 by its sum of digits (36), we get a square (4614419534400 = 2148120²).

128178320400 divided by its sum of digits (36) gives a square (3560508900 = 59670²).

The spelling of 128178320400 in words is "one hundred twenty-eight billion, one hundred seventy-eight million, three hundred twenty thousand, four hundred".