26782813360800 has 1440 divisors, whose sum is σ = 113299114642560. Its totient is φ = 6030493286400.

The previous prime is 26782813360781. The next prime is 26782813360811. The reversal of 26782813360800 is 806331828762.

26782813360800 is a `hidden beast` number, since 2 + 6 + 7 + 8 + 28 + 1 + 3 + 3 + 608 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1440).

It is a hoax number, since the sum of its digits (54) coincides with the sum of the digits of its distinct prime factors.

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

It is an unprimeable number.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 12393711720 + ... + 12393713880.

It is an arithmetic number, because the mean of its divisors is an integer number (78679940724).

Almost surely, 2^{26782813360800} is an apocalyptic number.

26782813360800 is a gapful number since it is divisible by the number (20) 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 26782813360800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (56649557321280).

26782813360800 is an abundant number, since it is smaller than the sum of its proper divisors (86516301281760).

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

26782813360800 is a wasteful number, since it uses less digits than its factorization.

26782813360800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2596 (or 2574 counting only the distinct ones).

The product of its (nonzero) digits is 4644864, while the sum is 54.

The spelling of 26782813360800 in words is "twenty-six trillion, seven hundred eighty-two billion, eight hundred thirteen million, three hundred sixty thousand, eight hundred".