442368000 has 288 divisors, whose sum is σ = 1635772320. Its totient is φ = 117964800.

The previous prime is 442367987. The next prime is 442368029. The reversal of 442368000 is 863244.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as (5!)³ ⋅ (2!)⁸.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 88473598 + ... + 88473602.

It is an arithmetic number, because the mean of its divisors is an integer number (5679765).

Almost surely, 2^442368000 is an apocalyptic number.

442368000 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 442368000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (817886160).

442368000 is an abundant number, since it is smaller than the sum of its proper divisors (1193404320).

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

442368000 is an frugal number, since it uses more digits than its factorization.

442368000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 58 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 27.

The square root of 442368000 is about 21032.5462081984. The cubic root of 442368000 is about 761.9525049447.

The spelling of 442368000 in words is "four hundred forty-two million, three hundred sixty-eight thousand".