78386400 has 288 divisors, whose sum is σ = 299980800. Its totient is φ = 19699200.

The previous prime is 78386389. The next prime is 78386443. The reversal of 78386400 is 468387.

78386400 is a `hidden beast` number, since 7 + 8 + 3 + 8 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×78386400² = 12288855409920000, which contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 410305 + ... + 410495.

It is an arithmetic number, because the mean of its divisors is an integer number (1041600).

Almost surely, 2^78386400 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 78386400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149990400).

78386400 is an abundant number, since it is smaller than the sum of its proper divisors (221594400).

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

78386400 is a wasteful number, since it uses less digits than its factorization.

78386400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 239 (or 220 counting only the distinct ones).

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

The square root of 78386400 is about 8853.6094334458. The cubic root of 78386400 is about 427.9702427851.

The spelling of 78386400 in words is "seventy-eight million, three hundred eighty-six thousand, four hundred".