137829340800 has 960 divisors, whose sum is σ = 528909004800. Its totient is φ = 35324190720.

The previous prime is 137829340793. The next prime is 137829340813. The reversal of 137829340800 is 8043928731.

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 an unprimeable number.

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 119 ways as a sum of consecutive naturals, for example, 1085270337 + ... + 1085270463.

It is an arithmetic number, because the mean of its divisors is an integer number (550946880).

Almost surely, 2^137829340800 is an apocalyptic number.

137829340800 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 137829340800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (264454502400).

137829340800 is an abundant number, since it is smaller than the sum of its proper divisors (391079664000).

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

137829340800 is a wasteful number, since it uses less digits than its factorization.

137829340800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 295 (or 269 counting only the distinct ones).

The product of its (nonzero) digits is 290304, while the sum is 45.

The spelling of 137829340800 in words is "one hundred thirty-seven billion, eight hundred twenty-nine million, three hundred forty thousand, eight hundred".