1012112000 has 192 divisors, whose sum is σ = 2708779320. Its totient is φ = 374784000.

The previous prime is 1012111993. The next prime is 1012112021. The reversal of 1012112000 is 2112101.

It can be written as a sum of positive squares in 12 ways, for example, as 389509696 + 622602304 = 19736^2 + 24952^2 .

It is a super-3 number, since 3×1012112000³ (a number of 28 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (8).

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 23 ways as a sum of consecutive naturals, for example, 16591970 + ... + 16592030.

Almost surely, 2^1012112000 is an apocalyptic number.

1012112000 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 1012112000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1354389660).

1012112000 is an abundant number, since it is smaller than the sum of its proper divisors (1696667320).

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

1012112000 is an frugal number, since it uses more digits than its factorization.

1012112000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 168 (or 85 counting only the distinct ones).

The product of its (nonzero) digits is 4, while the sum is 8.

The square root of 1012112000 is about 31813.7077373889. The cubic root of 1012112000 is about 1004.0211420763.

Adding to 1012112000 its reverse (2112101), we get a palindrome (1014224101).

The spelling of 1012112000 in words is "one billion, twelve million, one hundred twelve thousand".