448199713382400 has 4032 divisors, whose sum is σ = 1963824659177472. Its totient is φ = 95551488000000.

The previous prime is 448199713382389. The next prime is 448199713382413. The reversal of 448199713382400 is 4283317991844.

448199713382400 is a `hidden beast` number, since 4 + 4 + 8 + 1 + 9 + 97 + 133 + 8 + 2 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (4032).

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 2476241510310 + ... + 2476241510490.

It is an arithmetic number, because the mean of its divisors is an integer number (487059687296).

Almost surely, 2^{448199713382400} is an apocalyptic number.

448199713382400 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 448199713382400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (981912329588736).

448199713382400 is an abundant number, since it is smaller than the sum of its proper divisors (1515624945795072).

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

448199713382400 is a wasteful number, since it uses less digits than its factorization.

448199713382400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 453 (or 421 counting only the distinct ones).

The product of its (nonzero) digits is 41803776, while the sum is 63.

The spelling of 448199713382400 in words is "four hundred forty-eight trillion, one hundred ninety-nine billion, seven hundred thirteen million, three hundred eighty-two thousand, four hundred".