86361513638400 has 7200 divisors, whose sum is σ = 445736158167168. Its totient is φ = 16023984537600.

The previous prime is 86361513638377. The next prime is 86361513638417. The reversal of 86361513638400 is 483631516368.

86361513638400 is a `hidden beast` number, since 8 + 6 + 3 + 61 + 513 + 63 + 8 + 4 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (7200).

It is a super-3 number, since 3×86361513638400³ (a number of 43 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 719 ways as a sum of consecutive naturals, for example, 499199500714 + ... + 499199500886.

Almost surely, 2^{86361513638400} is an apocalyptic number.

86361513638400 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 86361513638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (222868079083584).

86361513638400 is an abundant number, since it is smaller than the sum of its proper divisors (359374644528768).

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

86361513638400 is a wasteful number, since it uses less digits than its factorization.

86361513638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 294 (or 251 counting only the distinct ones).

The product of its (nonzero) digits is 7464960, while the sum is 54.

The spelling of 86361513638400 in words is "eighty-six trillion, three hundred sixty-one billion, five hundred thirteen million, six hundred thirty-eight thousand, four hundred".