849072000 has 576 divisors, whose sum is σ = 3455609040. Its totient is φ = 183859200.

The previous prime is 849071999. The next prime is 849072011. The reversal of 849072000 is 270948.

849072000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a super-2 number, since 2×849072000² = 1441846522368000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 44687991 + ... + 44688009.

Almost surely, 2^849072000 is an apocalyptic number.

849072000 is a gapful number since it is divisible by the number (80) 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 849072000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1727804520).

849072000 is an abundant number, since it is smaller than the sum of its proper divisors (2606537040).

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

849072000 is a wasteful number, since it uses less digits than its factorization.

849072000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 84 (or 36 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 30.

The square root of 849072000 is about 29138.8400592748. The cubic root of 849072000 is about 946.9233803118.

Multiplying 849072000 by its sum of digits (30), we get a square (25472160000 = 159600²).

849072000 divided by its sum of digits (30) gives a square (28302400 = 5320²).

The spelling of 849072000 in words is "eight hundred forty-nine million, seventy-two thousand".