442961438400 has 2016 divisors, whose sum is σ = 1917259787520. Its totient is φ = 99028500480.

The previous prime is 442961438369. The next prime is 442961438473. The reversal of 442961438400 is 4834169244.

442961438400 is a `hidden beast` number, since 4 + 4 + 29 + 614 + 3 + 8 + 4 + 0 + 0 = 666.

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

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, 5336884759 + ... + 5336884841.

It is an arithmetic number, because the mean of its divisors is an integer number (951021720).

Almost surely, 2^442961438400 is an apocalyptic number.

442961438400 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 442961438400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (958629893760).

442961438400 is an abundant number, since it is smaller than the sum of its proper divisors (1474298349120).

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

442961438400 is a wasteful number, since it uses less digits than its factorization.

442961438400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 200 (or 166 counting only the distinct ones).

The product of its (nonzero) digits is 663552, while the sum is 45.

The spelling of 442961438400 in words is "four hundred forty-two billion, nine hundred sixty-one million, four hundred thirty-eight thousand, four hundred".