78336000 has 312 divisors, whose sum is σ = 299004264. Its totient is φ = 19660800.

The previous prime is 78335963. The next prime is 78336001. The reversal of 78336000 is 63387.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 331776 + 78004224 = 576^2 + 8832^2 .

It is a super-3 number, since 3×78336000³ (a number of 25 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (78336001) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 4607992 + ... + 4608008.

It is an arithmetic number, because the mean of its divisors is an integer number (958347).

Almost surely, 2^78336000 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 78336000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149502132).

78336000 is an abundant number, since it is smaller than the sum of its proper divisors (220668264).

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

78336000 is a wasteful number, since it uses less digits than its factorization.

78336000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 3024, while the sum is 27.

The square root of 78336000 is about 8850.7626790012. The cubic root of 78336000 is about 427.8784992991.

Adding to 78336000 its reverse (63387), we get a palindrome (78399387).

The spelling of 78336000 in words is "seventy-eight million, three hundred thirty-six thousand".