127405313538048 has 5760 divisors, whose sum is σ = 546607885824000. Its totient is φ = 29135559720960.

The previous prime is 127405313538047. The next prime is 127405313538053. The reversal of 127405313538048 is 840835313504721.

127405313538048 is a `hidden beast` number, since 1 + 2 + 7 + 4 + 0 + 53 + 13 + 538 + 0 + 48 = 666.

It is a super-3 number, since 3×127405313538048³ (a number of 43 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

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

It is a junction number, because it is equal to n+sod(n) for n = 127405313537985 and 127405313538003.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (127405313538047) by changing a digit.

It is a polite number, since it can be written in 479 ways as a sum of consecutive naturals, for example, 1431520376788 + ... + 1431520376876.

It is an arithmetic number, because the mean of its divisors is an integer number (94897202400).

Almost surely, 2^{127405313538048} is an apocalyptic number.

127405313538048 is a gapful number since it is divisible by the number (18) 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 127405313538048, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (273303942912000).

127405313538048 is an abundant number, since it is smaller than the sum of its proper divisors (419202572285952).

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

127405313538048 is a wasteful number, since it uses less digits than its factorization.

127405313538048 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 223 (or 187 counting only the distinct ones).

The product of its (nonzero) digits is 9676800, while the sum is 54.

The spelling of 127405313538048 in words is "one hundred twenty-seven trillion, four hundred five billion, three hundred thirteen million, five hundred thirty-eight thousand, forty-eight".