827148672 has 384 divisors, whose sum is σ = 2940537600. Its totient is φ = 226437120.

The previous prime is 827148667. The next prime is 827148677. The reversal of 827148672 is 276841728.

It is an interprime number because it is at equal distance from previous prime (827148667) and next prime (827148677).

It is a tau number, because it is divible by the number of its divisors (384).

It is a nude number because it is divisible by every one of its digits.

Its product of digits (301056) is a multiple of the sum of its prime factors (196).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (827148677) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 6314047 + ... + 6314177.

It is an arithmetic number, because the mean of its divisors is an integer number (7657650).

Almost surely, 2^827148672 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 827148672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1470268800).

827148672 is an abundant number, since it is smaller than the sum of its proper divisors (2113388928).

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

827148672 is a wasteful number, since it uses less digits than its factorization.

827148672 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 196 (or 172 counting only the distinct ones).

The product of its digits is 301056, while the sum is 45.

The square root of 827148672 is about 28760.1924889247. The cubic root of 827148672 is about 938.7022502150.

The spelling of 827148672 in words is "eight hundred twenty-seven million, one hundred forty-eight thousand, six hundred seventy-two".