8585438400 has 1344 divisors, whose sum is σ = 40818816000. Its totient is φ = 1703116800.

The previous prime is 8585438377. The next prime is 8585438453. The reversal of 8585438400 is 48345858.

It is a tau number, because it is divible by the number of its divisors (1344).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 96465556 + ... + 96465644.

Almost surely, 2^8585438400 is an apocalyptic number.

8585438400 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 8585438400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20409408000).

8585438400 is an abundant number, since it is smaller than the sum of its proper divisors (32233377600).

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

8585438400 is a wasteful number, since it uses less digits than its factorization.

8585438400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 167 (or 146 counting only the distinct ones).

The product of its (nonzero) digits is 614400, while the sum is 45.

The square root of 8585438400 is about 92657.6408074369. The cubic root of 8585438400 is about 2047.6426124015.

It can be divided in two parts, 8585 and 438400, that added together give a triangular number (446985 = T₉₄₅).

The spelling of 8585438400 in words is "eight billion, five hundred eighty-five million, four hundred thirty-eight thousand, four hundred".