135766540800 has 960 divisors, whose sum is σ = 552384645120. Its totient is φ = 32385024000.

The previous prime is 135766540711. The next prime is 135766540801. The reversal of 135766540800 is 8045667531.

135766540800 is a `hidden beast` number, since 1 + 35 + 76 + 6 + 540 + 8 + 0 + 0 = 666.

135766540800 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (960).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (135766540801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 269913349 + ... + 269913851.

It is an arithmetic number, because the mean of its divisors is an integer number (575400672).

Almost surely, 2^135766540800 is an apocalyptic number.

135766540800 is a gapful number since it is divisible by the number (10) 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 135766540800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (276192322560).

135766540800 is an abundant number, since it is smaller than the sum of its proper divisors (416618104320).

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

135766540800 is a wasteful number, since it uses less digits than its factorization.

135766540800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 622 (or 595 counting only the distinct ones).

The product of its (nonzero) digits is 604800, while the sum is 45.

The spelling of 135766540800 in words is "one hundred thirty-five billion, seven hundred sixty-six million, five hundred forty thousand, eight hundred".