86378400 has 360 divisors, whose sum is σ = 332728704. Its totient is φ = 21772800.

The previous prime is 86378399. The next prime is 86378401. The reversal of 86378400 is 487368.

It is an interprime number because it is at equal distance from previous prime (86378399) and next prime (86378401).

It is a tau number, because it is divible by the number of its divisors (360).

It is a super-2 number, since 2×86378400² = 14922455973120000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (86378401) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 2008779 + ... + 2008821.

Almost surely, 2^86378400 is an apocalyptic number.

86378400 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 86378400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (166364352).

86378400 is an abundant number, since it is smaller than the sum of its proper divisors (246350304).

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

86378400 is a wasteful number, since it uses less digits than its factorization.

86378400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 106 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The square root of 86378400 is about 9293.9980632664. The cubic root of 86378400 is about 442.0469364514.

Adding to 86378400 its sum of digits (36), we get a square (86378436 = 9294²).

The spelling of 86378400 in words is "eighty-six million, three hundred seventy-eight thousand, four hundred".