84564000 has 336 divisors, whose sum is σ = 322260120. Its totient is φ = 21772800.

The previous prime is 84563993. The next prime is 84564013. The reversal of 84564000 is 46548.

It can be written as a sum of positive squares in 4 ways, for example, as 25765776 + 58798224 = 5076^2 + 7668^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 2915986 + ... + 2916014.

Almost surely, 2^84564000 is an apocalyptic number.

84564000 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 84564000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (161130060).

84564000 is an abundant number, since it is smaller than the sum of its proper divisors (237696120).

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

84564000 is an equidigital number, since it uses as much as digits as its factorization.

84564000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 72 (or 39 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 84564000 is about 9195.8686376003. The cubic root of 84564000 is about 438.9299064966.

The spelling of 84564000 in words is "eighty-four million, five hundred sixty-four thousand".