137305947824640 has 480 divisors, whose sum is σ = 544218162808320. Its totient is φ = 31340540362752.

The previous prime is 137305947824629. The next prime is 137305947824677. The reversal of 137305947824640 is 46428749503731.

137305947824640 is a `hidden beast` number, since 1 + 3 + 7 + 3 + 0 + 5 + 94 + 7 + 82 + 464 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (480).

It is a super-2 number, since 2×137305947824640² (a number of 29 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is an unprimeable number.

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 47 ways as a sum of consecutive naturals, for example, 115368282 + ... + 116552358.

It is an arithmetic number, because the mean of its divisors is an integer number (1133787839184).

It is a 1-persistent number, because it is pandigital, but 2⋅137305947824640 = 274611895649280 is not.

Almost surely, 2^{137305947824640} is an apocalyptic number.

137305947824640 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 137305947824640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (272109081404160).

137305947824640 is an abundant number, since it is smaller than the sum of its proper divisors (406912214983680).

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

137305947824640 is a wasteful number, since it uses less digits than its factorization.

137305947824640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1184832 (or 1184813 counting only the distinct ones).

The product of its (nonzero) digits is 121927680, while the sum is 63.

The spelling of 137305947824640 in words is "one hundred thirty-seven trillion, three hundred five billion, nine hundred forty-seven million, eight hundred twenty-four thousand, six hundred forty".