85782400 has 96 divisors (see below), whose sum is σ = 231268680. Its totient is φ = 31180800.

The previous prime is 85782371. The next prime is 85782407. The reversal of 85782400 is 428758.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (85782407) by changing a digit.

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 11 ways as a sum of consecutive naturals, for example, 33982 + ... + 36418.

Almost surely, 2^85782400 is an apocalyptic number.

85782400 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 85782400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (115634340).

85782400 is an abundant number, since it is smaller than the sum of its proper divisors (145486280).

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

85782400 is a wasteful number, since it uses less digits than its factorization.

85782400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2472 (or 2455 counting only the distinct ones).

The product of its (nonzero) digits is 17920, while the sum is 34.

The square root of 85782400 is about 9261.8788590653. The cubic root of 85782400 is about 441.0278998465.

The spelling of 85782400 in words is "eighty-five million, seven hundred eighty-two thousand, four hundred".