1029152000 has 144 divisors (see below), whose sum is σ = 2654542800. Its totient is φ = 397107200.

The previous prime is 1029151999. The next prime is 1029152009. The reversal of 1029152000 is 2519201.

1029152000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 8 ways, for example, as 653722624 + 375429376 = 25568^2 + 19376^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1029152009) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 927446 + ... + 928554.

It is an arithmetic number, because the mean of its divisors is an integer number (18434325).

Almost surely, 2^1029152000 is an apocalyptic number.

1029152000 is a gapful number since it is divisible by the number (10) 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 1029152000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1327271400).

1029152000 is an abundant number, since it is smaller than the sum of its proper divisors (1625390800).

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

1029152000 is an equidigital number, since it uses as much as digits as its factorization.

1029152000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1169 (or 1145 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 20.

The square root of 1029152000 is about 32080.3990000125. The cubic root of 1029152000 is about 1009.6244069570.

The spelling of 1029152000 in words is "one billion, twenty-nine million, one hundred fifty-two thousand".