6829371648000 has 2304 divisors, whose sum is σ = 28887460842240. Its totient is φ = 1546321920000.

The previous prime is 6829371647981. The next prime is 6829371648019. The reversal of 6829371648000 is 8461739286.

6829371648000 is a `hidden beast` number, since 6 + 8 + 2 + 93 + 71 + 6 + 480 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (6829371647981) and next prime (6829371648019).

It is a tau number, because it is divible by the number of its divisors (2304).

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, 52132607935 + ... + 52132608065.

It is an arithmetic number, because the mean of its divisors is an integer number (12537960435).

Almost surely, 2^{6829371648000} is an apocalyptic number.

6829371648000 is a gapful number since it is divisible by the number (60) 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 6829371648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (14443730421120).

6829371648000 is an abundant number, since it is smaller than the sum of its proper divisors (22058089194240).

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

6829371648000 is a wasteful number, since it uses less digits than its factorization.

6829371648000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 224 (or 169 counting only the distinct ones).

The product of its (nonzero) digits is 3483648, while the sum is 54.

The spelling of 6829371648000 in words is "six trillion, eight hundred twenty-nine billion, three hundred seventy-one million, six hundred forty-eight thousand".