448191313920 has 1152 divisors, whose sum is σ = 1863678136320. Its totient is φ = 97462517760.

The previous prime is 448191313903. The next prime is 448191313939. The reversal of 448191313920 is 29313191844.

448191313920 is a `hidden beast` number, since 4 + 48 + 191 + 31 + 392 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1459906407 + ... + 1459906713.

It is an arithmetic number, because the mean of its divisors is an integer number (1617776160).

Almost surely, 2^448191313920 is an apocalyptic number.

448191313920 is a gapful number since it is divisible by the number (40) 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 448191313920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (931839068160).

448191313920 is an abundant number, since it is smaller than the sum of its proper divisors (1415486822400).

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

448191313920 is a wasteful number, since it uses less digits than its factorization.

448191313920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 451 (or 428 counting only the distinct ones).

The product of its (nonzero) digits is 186624, while the sum is 45.

The spelling of 448191313920 in words is "four hundred forty-eight billion, one hundred ninety-one million, three hundred thirteen thousand, nine hundred twenty".