84164000 has 96 divisors (see below), whose sum is σ = 211223376. Its totient is φ = 32947200.

The previous prime is 84163999. The next prime is 84164009. The reversal of 84164000 is 46148.

It is a happy number.

It can be written as a sum of positive squares in 8 ways, for example, as 11641744 + 72522256 = 3412^2 + 8516^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (84164009) 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, 211802 + ... + 212198.

Almost surely, 2^84164000 is an apocalyptic number.

84164000 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 84164000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (105611688).

84164000 is an abundant number, since it is smaller than the sum of its proper divisors (127059376).

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

84164000 is a wasteful number, since it uses less digits than its factorization.

84164000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 475 (or 457 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 23.

The square root of 84164000 is about 9174.0939607135. The cubic root of 84164000 is about 438.2367450279.

The spelling of 84164000 in words is "eighty-four million, one hundred sixty-four thousand".