3117438640800 has 2592 divisors, whose sum is σ = 13519698558912. Its totient is φ = 694241280000.

The previous prime is 3117438640753. The next prime is 3117438640807. The reversal of 3117438640800 is 80468347113.

It is a tau number, because it is divible by the number of its divisors (2592).

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 (3117438640807) by changing a digit.

It is a polite number, since it can be written in 431 ways as a sum of consecutive naturals, for example, 76035088780 + ... + 76035088820.

It is an arithmetic number, because the mean of its divisors is an integer number (5215933086).

Almost surely, 2^{3117438640800} is an apocalyptic number.

3117438640800 is a gapful number since it is divisible by the number (30) 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 3117438640800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6759849279456).

3117438640800 is an abundant number, since it is smaller than the sum of its proper divisors (10402259918112).

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

3117438640800 is a wasteful number, since it uses less digits than its factorization.

3117438640800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 186 (or 130 counting only the distinct ones).

The product of its (nonzero) digits is 387072, while the sum is 45.

The spelling of 3117438640800 in words is "three trillion, one hundred seventeen billion, four hundred thirty-eight million, six hundred forty thousand, eight hundred".