84096000 has 264 divisors, whose sum is σ = 307197384. Its totient is φ = 22118400.

The previous prime is 84095989. The next prime is 84096017. The reversal of 84096000 is 69048.

It can be written as a sum of positive squares in 4 ways, for example, as 2663424 + 81432576 = 1632^2 + 9024^2 .

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1151964 + ... + 1152036.

Almost surely, 2^84096000 is an apocalyptic number.

84096000 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 84096000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (153598692).

84096000 is an abundant number, since it is smaller than the sum of its proper divisors (223101384).

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

84096000 is a wasteful number, since it uses less digits than its factorization.

84096000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 114 (or 83 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 84096000 is about 9170.3871237805. The cubic root of 84096000 is about 438.1186892958.

It can be divided in two parts, 8 and 4096000, that multiplied together give a cube (32768000 = 320³).

The spelling of 84096000 in words is "eighty-four million, ninety-six thousand".