442828800 has 324 divisors, whose sum is σ = 1638733005. Its totient is φ = 114278400.

The previous prime is 442828777. The next prime is 442828817. The reversal of 442828800 is 8828244.

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 can be written as a sum of positive squares in 2 ways, for example, as 433972224 + 8856576 = 20832^2 + 2976^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=14880.

It is a super-2 number, since 2×442828800² = 392194692218880000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 14284785 + ... + 14284815.

Almost surely, 2^442828800 is an apocalyptic number.

442828800 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 442828800

442828800 is an abundant number, since it is smaller than the sum of its proper divisors (1195904205).

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

442828800 is a wasteful number, since it uses less digits than its factorization.

442828800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 100 (or 41 counting only the distinct ones).

The product of its (nonzero) digits is 32768, while the sum is 36.

The square root of 442828800 is about 21043.4978081117. The cubic root of 442828800 is about 762.2169799764.

Multiplying 442828800 by its product of nonzero digits (32768), we get a square (14510614118400 = 3809280²).

The spelling of 442828800 in words is "four hundred forty-two million, eight hundred twenty-eight thousand, eight hundred".