86123724724800 has 2520 divisors, whose sum is σ = 403375940490600. Its totient is φ = 17887928647680.

The previous prime is 86123724724777. The next prime is 86123724724801. The reversal of 86123724724800 is 842742732168.

86123724724800 is a `hidden beast` number, since 8 + 6 + 1 + 23 + 72 + 4 + 72 + 480 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 31710323340864 + 54413401383936 = 5631192^2 + 7376544^2 .

It is a tau number, because it is divible by the number of its divisors (2520).

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

It is not an unprimeable number, because it can be changed into a prime (86123724724801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 359 ways as a sum of consecutive naturals, for example, 3130733446 + ... + 3130760954.

It is an arithmetic number, because the mean of its divisors is an integer number (160069817655).

Almost surely, 2^{86123724724800} is an apocalyptic number.

86123724724800 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 86123724724800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (201687970245300).

86123724724800 is an abundant number, since it is smaller than the sum of its proper divisors (317252215765800).

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

86123724724800 is a wasteful number, since it uses less digits than its factorization.

86123724724800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 27603 (or 27572 counting only the distinct ones).

The product of its (nonzero) digits is 7225344, while the sum is 54.

The spelling of 86123724724800 in words is "eighty-six trillion, one hundred twenty-three billion, seven hundred twenty-four million, seven hundred twenty-four thousand, eight hundred".