137381134464000 has 2112 divisors, whose sum is σ = 572487863980032. Its totient is φ = 31032336384000.

The previous prime is 137381134463831. The next prime is 137381134464047. The reversal of 137381134464000 is 464431183731.

137381134464000 is a `hidden beast` number, since 1 + 3 + 73 + 8 + 1 + 134 + 46 + 400 + 0 = 666.

It is a super-2 number, since 2×137381134464000² (a number of 29 digits) contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 447495551847 + ... + 447495552153.

It is an arithmetic number, because the mean of its divisors is an integer number (271064329536).

Almost surely, 2^{137381134464000} is an apocalyptic number.

137381134464000 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 137381134464000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (286243931990016).

137381134464000 is an abundant number, since it is smaller than the sum of its proper divisors (435106729516032).

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

137381134464000 is a wasteful number, since it uses less digits than its factorization.

137381134464000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 829 (or 798 counting only the distinct ones).

The product of its (nonzero) digits is 580608, while the sum is 45.

The spelling of 137381134464000 in words is "one hundred thirty-seven trillion, three hundred eighty-one billion, one hundred thirty-four million, four hundred sixty-four thousand".